LeePappas
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Moderator note:
I have merged all of LeePappas’ content into one mega thread of sorts to keep things a bit cleaner. It may look a bit messy in terms of the posts and replies but hopefully people should understand what is going on here, especially if you’ve already read through the individual threads.
-Trismegistus
In this post I aim to show that Rome was founded on April 1st 685 BC. The first king of Rome changed the month names of the calendar previously in use, to commemorate the event. Simply by performing an in depth etymology of the word 'April' a fantastic amount of history can be uncovered.
To begin with, I used my limited knowledge of Greek to wonder why Roman month names are built from Greek words. The etymology of the last month reveals it is derived from the Greek word for ten.
deka [Greek] = decem [Latin] = ten
The other equations are:
Ena[Greek]= Unum [Latin]=one
Hexi [Greek]=Sextem [Latin]=six
Epta[Greek]=Septem[Latin]=seven
Octo[Greek]=Octem [Latin]=eight
Enneia [Greek]=Novem[Latin]=nine
March, April, and May, aren't derivatives of numbers, so I began to wonder about their etymologies. March and May proved elusive initially, but I found success with April.
I used the Scott-Liddell Greek English dictionary to look up all words starting with 'apr', and there was only one: aperro. It's last letter is actually omega not omicron, so if you look it up in Perseus Digital Library you have to enter aperrw. Here's what you will find:
Aperro = gone
Then I researched the Roman word for the month of April, and discovered it was Aprilis.
Then I asked myself what was gone+Ilis? It meant nothing to me, but I knew enough Greek to solve the problem.
Helios[Greek]=ilius[Latin]=sun.
Thus the etymology of April is
Aperrilius=Aprilius=Aprilis=April=gone+sun
It was then I suspected there was an ancient eclipse and the people who lived through it changed the month names of the previous calendar to commemorate the eclipse event. Subsequently I reconstructed that new calendar as:
Unius
Martius
Aprilius
Maius
Quinctilius
Sextilius
Septembrilius
Octobrilius
Novembrilius
Decembrilius
The words Quinctilius, sextilius, septembrilius, Octobrilius, and Decembrilius all can be found in extant Latin documents.
Then I found the following passage in Plutarch's the life of Romulus:
"At the present time, indeed, there is no agreement between the Roman and Greek months, but they say that the day on which Romulus founded his city was precisely the thirtieth of the month, and that on that day there was a conjunction of the sun and moon, with an eclipse, which they think was the one seen by Antimachus, the epic poet of Teos, in the third year of the sixth Olympiad."
I then learned about eclipses and found out they can only occur on a new moon, when the sun, moon, and earth are in a straight line.
Thus I was off and running. Rome was founded on the day of a solar eclipse, and the Romans who apparently spoke Greek at that time, renamed the month the eclipse happened in Aprilius to commemorate the event. The new moon was always at the start of the month, so that eclipse happened April 1st. The only thing left was to find the year, and I knew the only way to do that is to use astronomy software.
You may wonder why I decided the founders of Rome spoke Greek, and not proto-Latin. Again, we can go to the word 'aperro'. The fact that the word has double R, indicates the word breaks there, that is aperro=aper+ro.
Now in Greek when you want to convert a word to it's opposite, you prefix it with the letter 'a'. For example:
Abaris(ahvareece)= light, not heavy
Barus(vareece)=heavy
Thus, aperro is actually composed of three Greek words: aperro=a+per+ro.
In my Divry Greek English dictionary, it has
Pera=over, across, through
Therefore aperro=not+through+ro.
I looked up 'per' in Perseus Digital Library and it meant 'at' in ancient Greek. Thus I concluded:
Aperro= not+at+Ro.
And I guessed that the Romans somehow knew, prior to renaming the month Aperrilius, that the eclipse wasn't visible at the island of Rhodes.
Then I performed an etymology on Rhodes, and came up with: Ro+edo.
Ro shows up in Romani, and in modern Greek edo=here.
Mani [Latin]=hands
So, Romani=Romans=row+hands, and Rhodes= row+here.
Since it is Greek and not Latin in which prefixing a word with 'a' means the opposite, I decided they spoke Greek rather than some form of ancient Latin.
Then, on a hunch, I performed an etymology on
'Hiroshima'.
Hi=day
Shima = island
So, Hiroshima=day+Ro+island.
So there may be a connection.
As to how determined the eclipse happened in 685 BC, that's really complicated. For starters I went looking for an ancient Historian I could trust. I decided I would need to know when he wrote, and I found Dionysius of Halicarnassus author of 'Roman Antiquities'. I wanted information on Rome obviously, and he fit the bill. I started from the beginning, and he said this:
"For from the very beginning, immediately after her founding, she began to draw to herself the neighbouring nations, which were both numerous and warlike, and continually advanced, subjugating every rival. And it is now seven hundred and forty-five years from her foundation down to the consulship of Claudius Nero, consul for the second time, and of Calpurnius Piso, who were chosen in the one hundred and ninety-third Olympiad.9 5 From the time that she mastered the whole of Italy she was emboldened to aspire to p13 govern all mankind, and after driving from off the sea the Carthaginians, whose maritime strength was superior to that of all others, and subduing Macedonia, which until then was reputed to be the most powerful nation on land, she no longer had as rival any nation either barbarian or Greek..."
Then I went to the consul list, having just discovered there was such a thing, and I found this:
7 BCTib. Claudius Nero II Cn. Calpurnius Piso
Many sources claimed Caesar was assassinated in 44 BC, so I felt I could trust Nero and Piso were consuls in 7 BC, I felt the list was right about that 7 BC date.
Now I was getting somewhere.
Then I thought about the calendar. I knew there was a point in time that the Romans changed from a ten month to a twelve month calendar. I needed to know when that change happened to find the year of the eclipse.
After a bit of searching I came across Censorinus's De Die Natali Liber. In it I found this:
"adeo aberratum est, ut C. Caesar pontifex maximus suo III et M. Aemilii Lepidi consulatu, quo retro delictum corrigeret, duos menses intercalarios dierum LXVII in mensem Novembrem et Decembrem interponeret, cum iam mense Februario dies III et XX intercalasset, faceretque eum annum dierum CCCCXLV, simul providens in futurum, ne iterum erraretur: nam intercalario mense sublato annum civilem ad solis cursum formavit."
Translation: so much so aberrated it is, that C. Caesar the Pontifex Maximus his 3rd and M. Ameilii Lepidus consuls, where back offense would correct, two intercalary months of days 67 in the months of November and December put in between, with already the month February days 3 and 20 intercalated, making his year of days 445, simultaneously providing in the future, no more mistakes, for intercalary month lifted up civil year to sun's course formed.
Then I went to the consul list and found 46 BC was the year of Caesar 3rd and Lepidus consuls. Then I read that that year was referred to as the Ultimus Anno Confusionis, or Last Year of Confusion. At this point I felt like I had enough information to figure out when the calendar change occurred.
445-67-23=355 days
If Ceasar didn't 'intercalate' 90 days, then that year would have had 355 days. How can a year have 355 days I thought. Then I reasoned that calendar was a compromise between a lunar and solar calendar, and I formulated this:
Ianuarius 30
Februarius 29
Martius 30
Aprilius 29
Maius 30
Unius 29
Quinctilius 30
Sextilius 29
Septembrilius 30
Octobrilius 29
Novembrilius 30
Decembrilius 29
The days add up to 354, so I knew I had the right idea with that calendar.
Then i came across something called the Octaeteris. It's a period of almost eight tropical years. The source mentioned the Octaeteris had a 22 or 23 day intercalary month. It didn't take me long to figure out how it worked.
Octaeteris
Year 1: 376 days
Year 2: 354 days
Year 3: 376 days
Year 4: 354 days
Year 5: 376 days
Year 6: 354 days
Year 7: 376 days
Year 8: 354 days
376*4+354*4=2920, and 2920/8= 365
Thus the Octaeteris had an average year of 365 days, with a 22 day intercalary month called Mercedinus intercalated every other year.
As of 46 BC the tropical year was thought to be about 365.25 days. According to Censorinus Julius Caesar added 90 days to the calendar in 46 BC. It made sense to me that he was trying to get the vernal equinox back to where it was when the Octaeteris was implemented. A better value was obtained by 1582, the year the intergravissimas Papal Bull of Pope Gregory XIII went into effect. It approximated the tropical year at 365.2425 days.
Slip rate=.2425 days per year
90 days/.2425 days per year=371 years
371+46=417
So the Octaeteris went into effect around 417 BC.
But could I get a better approximation?
I began to not trust Censorinus, because he claimed the intercalary month was 23 days, when now I knew it was 22. After some thought it occurred to me that Caesar would have waited until the end of an Octaeterian cycle to add the 90 days. With that one idea, I could improve on my date of 417 BC. Here's how I did it.
(417-46)/8=46.375
So that's not a whole number of Octaeterian cycles, the information in Censorinus is badly flawed.
Then I began to suspect the 90 days were added in 45 BC not 46 BC, because Caesar was assassinated in 44 BC, and I figured the events were related. So I did this:
(412 - 44)=368, 368/8=46
(420-44)=372, 372/8=47
Thus, the Octaeteris was implemented in 412 or 420 BC.
If 412 BC, then the vernal equinox slipped 368*.2425=89 days.
If 420 BC, then the vernal equinox slipped 372*.2425=90 days.
So what was this magical day the Romans were trying to get the vernal equinox on? Aprilius 1st the founding date of Rome of course. It's near to March 21st where it is today, so that's a good guess.
Then I used a spreadsheet with all the Roman consuls, from 44 BC backwards to the first consuls at Rome, Lucius Tarquinius Collatinus, and Lucius Junius Brutus. Eventually I ruled out 420 BC. Thus I could get the Julian day number of the day of implementation of the Octaeteris to within a few days, if I knew the precise time of year of one vernal equinox, and the precise value of one tropical year.
Modern sources place the value of one tropical year at 365.2422 days.
At this point I downloaded Home Planet astronomy software.
It has the 1582 vernal equinox on midnight March 21st, Julian day number 2298952.5 [exact value].
412 BC vernal equinox
2298952.5 - (1582+412)*365.2422=1570659.55
Aprilius 1, 412 BC=1570659.5
Therefore January 1st, 412 BC =
1570569.5 -30-29-30=1570570.5
Day 1 of the Octaeteris= 1570570.5
Now to find the year of the eclipse, we can make use of the following information in Dionysius of Halicarnassus' Roman Antiquities:
"74 1 As to the last settlement or founding of the city, or whatever we ought to call it, Timaeus of Sicily,196 following what principle I do not know, places it at the same time as the founding of Carthage, that is, in the thirty-eighth year before the first Olympiad;197 Lucius Cincius, a member of the senate, places it about the fourth year of the twelfth Olympiad,198 and Quintus Fabius in the first year of the eighth Olympiad.199 2 Porcius Cato does not give the time according to Greek reckoning, but being as careful as any writer in gathering the date of ancient history, he places its founding four hundred and thirty-two years after the Trojan war; and this p247 time, being compared with the Chronicles of Eratosthenes,200 corresponds to the first year of the seventh Olympiad.201 That the canons of Eratosthenes are sound I have shown in another treatise,202 where I have also shown how the Roman chronology is to be synchronized with that of the Greeks. 3 For I did not think it sufficient, like Polybius of Megalopolis,203 to say merely that I believe Rome was built in the second year of the seventh Olympiad,204 nor to let my belief rest without further examination upon the single tablet preserved by the high priests, the only one of its kind, but I determined to set forth the reasons that had appealed to me, so that all might examine them who so desired. 4 In that treatise, therefore, the detailed exposition is given; but in the course of the present work also the most essential of the conclusions there reached will be mentioned. The matter stands thus: It is generally agreed that the invasion of the Gauls,205 during which the city of Rome was taken, happened during the archonship of Pyrgion at Athens, in the first year of the ninety-eighth Olympiad.206 Now if the time before the taking of the city is reckoned back to Lucius Junius Brutus and Lucius Tarquinius Collatinus, the first consuls at Rome after the overthrow of the kings, it comprehends one hundred p249 and twenty years. 5 This is proved in many other ways, but particularly by the records of the censors, which receives in succession from the father and takes great care to transmit to posterity, like family rites; and there are many illustrious men of censorian families who preserve these records. In them I find that in the second year before the taking of the city there was a census of the Roman people, to which, as to the rest of them, there is affixed the date, as follows: "In the consulship of Lucius Valerius Potitus and Titus Manlius Capitolinus, in the one hundred and nineteenth year after the expulsion of the kings." 6 So that the Gallic invasion, which we find to have occurred in the second year after the census, happened when the hundred and twenty years were completed. If, now, this interval of time is found to consist of thirty Olympiads, it must be allowed that the first consuls to be chosen entered upon their magistracy in the first year of the sixty-eighth Olympiad, the same year that Isagoras was archon at Athens."
In the Roman Consul list, Lucius Valerius Potitus and Titus Manlius Capitolinus were consuls in the 117th year after the expulsion of the kings, so Dionysus lied there by two years. You discover this by actually counting the consuls, which I didn't do initially.
He continues:
"75 1 And, again, if from the expulsion of the kings the time is reckoned back to Romulus, the first ruler of the city, it amounts to two hundred and forty-four years. This is known from the order in which the kings succeeded one another and the number of years each of them ruled. For Romulus, the founder p251 of Rome, reigned thirty-seven years, it is said, and after his death the city was a year without a king. 2 Then Numa Pompilius, who was chosen by the people, reigned forty-three years; after Numa, Tullus Hostilius thirty-two; and his successor, Ancus Marcius, twenty-four; after Marcius, Lucius Tarquinius, called Priscus, thirty-eight; Servius Tullius, who succeeded him, forty-four. And the slayer of Servius, Lucius Tarquinius, the tyrannical prince who, from his contempt of justice, was called Superbus, extended his reign to the twenty-fifth year. 3 As the reigns, therefore, of the kings amount to two hundred and forty-four years or sixty-one Olympiads, it follows necessarily that Romulus, the first ruler of the city, began his reign in the first year of the seventh Olympiad, when Charops at Athens was in the first year of his ten-year term as archon.208 For the count of the years requires this; and that each king reigned the number of years is shown in that treatise of mine to which I have referred."
Olympiad 195, year 1= 1 BC, therefore
Olympiad 92, year 2=412 BC.
Now go back to the first consuls at Rome.
Correcting for Dionysius' 2-year lie, the first consuls of Rome took office on Unius 1, Olympiad 68 year 3. 92-68=24, there were four years per Olympiad, 24*4=96. So the first consuls of Rome took office 94 lunar years before Julian day number 1570570.5. The Roman kings ruled for 244 lunar years, according to Dionysius' sources. 94+244=338.
One 10-month lunar year=295.306 days.
Thus the eclipse happened 338 lunar years before 1570570.5.
338*295.306=99814
1570570.5-99814=1470757.5
The eclipse happened around 1470757.5
Using Fourmilab Calendar Converter you find:
September 12, 687 BC = 1470757.5.
Looking at all the new moons around that time, I found the Julian day number of the eclipse.
Eclipse visible from Rome on Julian day number 1470868.5.
The software says that was 686 BC, but I claimed at the start of the thread that the eclipse took place in 685 BC, how can this be?
The answer is there was a year zero between 1 BC and 1 AD.
PROOF THERE WAS A ZERO BC
To accomplish this proof let's find day one of the Julian calendar under the assumption that Julius Caesar added 89 days to the calendar in 45 BC.
(412-44)*365+89 = 134409
1570570.5 + 134409 = 1704979.5 = Ianuarius 1, 44 BC = day 1 of the Julian calendar
2451544.5 = January 1st, 2000
2451544.5 - 1704979.55 = 746565
746565/365.25= 2043.983
Therefore from day one of the Julian calendar to January 1st 2000, there were 2044 years.
Assume incorrectly that there was no zero BC.
From January 1, 1 AD to January 1, 2000 AD, there were 1999 years. From January 1, 44 BC to January 1, 1 AD there were 44 years. 1999+44=2043. Using Julian day numbers we know that this had to be 2044, therefore there was a 0 BC.
Q.E.D.
QED=quod erat demonstrandum= which was to be demonstrated
Therefore, the solar eclipse that marks the founding date of Rome occurred on Julian day number 1470868.5=Aprilius 1, 685 BC = January 8, 686 BC [Gregorian proleptic], which was to be demonstrated. Q.E.D.
I have merged all of LeePappas’ content into one mega thread of sorts to keep things a bit cleaner. It may look a bit messy in terms of the posts and replies but hopefully people should understand what is going on here, especially if you’ve already read through the individual threads.
-Trismegistus
In this post I aim to show that Rome was founded on April 1st 685 BC. The first king of Rome changed the month names of the calendar previously in use, to commemorate the event. Simply by performing an in depth etymology of the word 'April' a fantastic amount of history can be uncovered.
To begin with, I used my limited knowledge of Greek to wonder why Roman month names are built from Greek words. The etymology of the last month reveals it is derived from the Greek word for ten.
deka [Greek] = decem [Latin] = ten
The other equations are:
Ena[Greek]= Unum [Latin]=one
Hexi [Greek]=Sextem [Latin]=six
Epta[Greek]=Septem[Latin]=seven
Octo[Greek]=Octem [Latin]=eight
Enneia [Greek]=Novem[Latin]=nine
March, April, and May, aren't derivatives of numbers, so I began to wonder about their etymologies. March and May proved elusive initially, but I found success with April.
I used the Scott-Liddell Greek English dictionary to look up all words starting with 'apr', and there was only one: aperro. It's last letter is actually omega not omicron, so if you look it up in Perseus Digital Library you have to enter aperrw. Here's what you will find:
Aperro = gone
Then I researched the Roman word for the month of April, and discovered it was Aprilis.
Then I asked myself what was gone+Ilis? It meant nothing to me, but I knew enough Greek to solve the problem.
Helios[Greek]=ilius[Latin]=sun.
Thus the etymology of April is
Aperrilius=Aprilius=Aprilis=April=gone+sun
It was then I suspected there was an ancient eclipse and the people who lived through it changed the month names of the previous calendar to commemorate the eclipse event. Subsequently I reconstructed that new calendar as:
Unius
Martius
Aprilius
Maius
Quinctilius
Sextilius
Septembrilius
Octobrilius
Novembrilius
Decembrilius
The words Quinctilius, sextilius, septembrilius, Octobrilius, and Decembrilius all can be found in extant Latin documents.
Then I found the following passage in Plutarch's the life of Romulus:
"At the present time, indeed, there is no agreement between the Roman and Greek months, but they say that the day on which Romulus founded his city was precisely the thirtieth of the month, and that on that day there was a conjunction of the sun and moon, with an eclipse, which they think was the one seen by Antimachus, the epic poet of Teos, in the third year of the sixth Olympiad."
I then learned about eclipses and found out they can only occur on a new moon, when the sun, moon, and earth are in a straight line.
Thus I was off and running. Rome was founded on the day of a solar eclipse, and the Romans who apparently spoke Greek at that time, renamed the month the eclipse happened in Aprilius to commemorate the event. The new moon was always at the start of the month, so that eclipse happened April 1st. The only thing left was to find the year, and I knew the only way to do that is to use astronomy software.
You may wonder why I decided the founders of Rome spoke Greek, and not proto-Latin. Again, we can go to the word 'aperro'. The fact that the word has double R, indicates the word breaks there, that is aperro=aper+ro.
Now in Greek when you want to convert a word to it's opposite, you prefix it with the letter 'a'. For example:
Abaris(ahvareece)= light, not heavy
Barus(vareece)=heavy
Thus, aperro is actually composed of three Greek words: aperro=a+per+ro.
In my Divry Greek English dictionary, it has
Pera=over, across, through
Therefore aperro=not+through+ro.
I looked up 'per' in Perseus Digital Library and it meant 'at' in ancient Greek. Thus I concluded:
Aperro= not+at+Ro.
And I guessed that the Romans somehow knew, prior to renaming the month Aperrilius, that the eclipse wasn't visible at the island of Rhodes.
Then I performed an etymology on Rhodes, and came up with: Ro+edo.
Ro shows up in Romani, and in modern Greek edo=here.
Mani [Latin]=hands
So, Romani=Romans=row+hands, and Rhodes= row+here.
Since it is Greek and not Latin in which prefixing a word with 'a' means the opposite, I decided they spoke Greek rather than some form of ancient Latin.
Then, on a hunch, I performed an etymology on
'Hiroshima'.
Hi=day
Shima = island
So, Hiroshima=day+Ro+island.
So there may be a connection.
As to how determined the eclipse happened in 685 BC, that's really complicated. For starters I went looking for an ancient Historian I could trust. I decided I would need to know when he wrote, and I found Dionysius of Halicarnassus author of 'Roman Antiquities'. I wanted information on Rome obviously, and he fit the bill. I started from the beginning, and he said this:
"For from the very beginning, immediately after her founding, she began to draw to herself the neighbouring nations, which were both numerous and warlike, and continually advanced, subjugating every rival. And it is now seven hundred and forty-five years from her foundation down to the consulship of Claudius Nero, consul for the second time, and of Calpurnius Piso, who were chosen in the one hundred and ninety-third Olympiad.9 5 From the time that she mastered the whole of Italy she was emboldened to aspire to p13 govern all mankind, and after driving from off the sea the Carthaginians, whose maritime strength was superior to that of all others, and subduing Macedonia, which until then was reputed to be the most powerful nation on land, she no longer had as rival any nation either barbarian or Greek..."
Then I went to the consul list, having just discovered there was such a thing, and I found this:
7 BCTib. Claudius Nero II Cn. Calpurnius Piso
Many sources claimed Caesar was assassinated in 44 BC, so I felt I could trust Nero and Piso were consuls in 7 BC, I felt the list was right about that 7 BC date.
Now I was getting somewhere.
Then I thought about the calendar. I knew there was a point in time that the Romans changed from a ten month to a twelve month calendar. I needed to know when that change happened to find the year of the eclipse.
After a bit of searching I came across Censorinus's De Die Natali Liber. In it I found this:
"adeo aberratum est, ut C. Caesar pontifex maximus suo III et M. Aemilii Lepidi consulatu, quo retro delictum corrigeret, duos menses intercalarios dierum LXVII in mensem Novembrem et Decembrem interponeret, cum iam mense Februario dies III et XX intercalasset, faceretque eum annum dierum CCCCXLV, simul providens in futurum, ne iterum erraretur: nam intercalario mense sublato annum civilem ad solis cursum formavit."
Translation: so much so aberrated it is, that C. Caesar the Pontifex Maximus his 3rd and M. Ameilii Lepidus consuls, where back offense would correct, two intercalary months of days 67 in the months of November and December put in between, with already the month February days 3 and 20 intercalated, making his year of days 445, simultaneously providing in the future, no more mistakes, for intercalary month lifted up civil year to sun's course formed.
Then I went to the consul list and found 46 BC was the year of Caesar 3rd and Lepidus consuls. Then I read that that year was referred to as the Ultimus Anno Confusionis, or Last Year of Confusion. At this point I felt like I had enough information to figure out when the calendar change occurred.
445-67-23=355 days
If Ceasar didn't 'intercalate' 90 days, then that year would have had 355 days. How can a year have 355 days I thought. Then I reasoned that calendar was a compromise between a lunar and solar calendar, and I formulated this:
Ianuarius 30
Februarius 29
Martius 30
Aprilius 29
Maius 30
Unius 29
Quinctilius 30
Sextilius 29
Septembrilius 30
Octobrilius 29
Novembrilius 30
Decembrilius 29
The days add up to 354, so I knew I had the right idea with that calendar.
Then i came across something called the Octaeteris. It's a period of almost eight tropical years. The source mentioned the Octaeteris had a 22 or 23 day intercalary month. It didn't take me long to figure out how it worked.
Octaeteris
Year 1: 376 days
Year 2: 354 days
Year 3: 376 days
Year 4: 354 days
Year 5: 376 days
Year 6: 354 days
Year 7: 376 days
Year 8: 354 days
376*4+354*4=2920, and 2920/8= 365
Thus the Octaeteris had an average year of 365 days, with a 22 day intercalary month called Mercedinus intercalated every other year.
As of 46 BC the tropical year was thought to be about 365.25 days. According to Censorinus Julius Caesar added 90 days to the calendar in 46 BC. It made sense to me that he was trying to get the vernal equinox back to where it was when the Octaeteris was implemented. A better value was obtained by 1582, the year the intergravissimas Papal Bull of Pope Gregory XIII went into effect. It approximated the tropical year at 365.2425 days.
Slip rate=.2425 days per year
90 days/.2425 days per year=371 years
371+46=417
So the Octaeteris went into effect around 417 BC.
But could I get a better approximation?
I began to not trust Censorinus, because he claimed the intercalary month was 23 days, when now I knew it was 22. After some thought it occurred to me that Caesar would have waited until the end of an Octaeterian cycle to add the 90 days. With that one idea, I could improve on my date of 417 BC. Here's how I did it.
(417-46)/8=46.375
So that's not a whole number of Octaeterian cycles, the information in Censorinus is badly flawed.
Then I began to suspect the 90 days were added in 45 BC not 46 BC, because Caesar was assassinated in 44 BC, and I figured the events were related. So I did this:
(412 - 44)=368, 368/8=46
(420-44)=372, 372/8=47
Thus, the Octaeteris was implemented in 412 or 420 BC.
If 412 BC, then the vernal equinox slipped 368*.2425=89 days.
If 420 BC, then the vernal equinox slipped 372*.2425=90 days.
So what was this magical day the Romans were trying to get the vernal equinox on? Aprilius 1st the founding date of Rome of course. It's near to March 21st where it is today, so that's a good guess.
Then I used a spreadsheet with all the Roman consuls, from 44 BC backwards to the first consuls at Rome, Lucius Tarquinius Collatinus, and Lucius Junius Brutus. Eventually I ruled out 420 BC. Thus I could get the Julian day number of the day of implementation of the Octaeteris to within a few days, if I knew the precise time of year of one vernal equinox, and the precise value of one tropical year.
Modern sources place the value of one tropical year at 365.2422 days.
At this point I downloaded Home Planet astronomy software.
It has the 1582 vernal equinox on midnight March 21st, Julian day number 2298952.5 [exact value].
412 BC vernal equinox
2298952.5 - (1582+412)*365.2422=1570659.55
Aprilius 1, 412 BC=1570659.5
Therefore January 1st, 412 BC =
1570569.5 -30-29-30=1570570.5
Day 1 of the Octaeteris= 1570570.5
Now to find the year of the eclipse, we can make use of the following information in Dionysius of Halicarnassus' Roman Antiquities:
"74 1 As to the last settlement or founding of the city, or whatever we ought to call it, Timaeus of Sicily,196 following what principle I do not know, places it at the same time as the founding of Carthage, that is, in the thirty-eighth year before the first Olympiad;197 Lucius Cincius, a member of the senate, places it about the fourth year of the twelfth Olympiad,198 and Quintus Fabius in the first year of the eighth Olympiad.199 2 Porcius Cato does not give the time according to Greek reckoning, but being as careful as any writer in gathering the date of ancient history, he places its founding four hundred and thirty-two years after the Trojan war; and this p247 time, being compared with the Chronicles of Eratosthenes,200 corresponds to the first year of the seventh Olympiad.201 That the canons of Eratosthenes are sound I have shown in another treatise,202 where I have also shown how the Roman chronology is to be synchronized with that of the Greeks. 3 For I did not think it sufficient, like Polybius of Megalopolis,203 to say merely that I believe Rome was built in the second year of the seventh Olympiad,204 nor to let my belief rest without further examination upon the single tablet preserved by the high priests, the only one of its kind, but I determined to set forth the reasons that had appealed to me, so that all might examine them who so desired. 4 In that treatise, therefore, the detailed exposition is given; but in the course of the present work also the most essential of the conclusions there reached will be mentioned. The matter stands thus: It is generally agreed that the invasion of the Gauls,205 during which the city of Rome was taken, happened during the archonship of Pyrgion at Athens, in the first year of the ninety-eighth Olympiad.206 Now if the time before the taking of the city is reckoned back to Lucius Junius Brutus and Lucius Tarquinius Collatinus, the first consuls at Rome after the overthrow of the kings, it comprehends one hundred p249 and twenty years. 5 This is proved in many other ways, but particularly by the records of the censors, which receives in succession from the father and takes great care to transmit to posterity, like family rites; and there are many illustrious men of censorian families who preserve these records. In them I find that in the second year before the taking of the city there was a census of the Roman people, to which, as to the rest of them, there is affixed the date, as follows: "In the consulship of Lucius Valerius Potitus and Titus Manlius Capitolinus, in the one hundred and nineteenth year after the expulsion of the kings." 6 So that the Gallic invasion, which we find to have occurred in the second year after the census, happened when the hundred and twenty years were completed. If, now, this interval of time is found to consist of thirty Olympiads, it must be allowed that the first consuls to be chosen entered upon their magistracy in the first year of the sixty-eighth Olympiad, the same year that Isagoras was archon at Athens."
In the Roman Consul list, Lucius Valerius Potitus and Titus Manlius Capitolinus were consuls in the 117th year after the expulsion of the kings, so Dionysus lied there by two years. You discover this by actually counting the consuls, which I didn't do initially.
He continues:
"75 1 And, again, if from the expulsion of the kings the time is reckoned back to Romulus, the first ruler of the city, it amounts to two hundred and forty-four years. This is known from the order in which the kings succeeded one another and the number of years each of them ruled. For Romulus, the founder p251 of Rome, reigned thirty-seven years, it is said, and after his death the city was a year without a king. 2 Then Numa Pompilius, who was chosen by the people, reigned forty-three years; after Numa, Tullus Hostilius thirty-two; and his successor, Ancus Marcius, twenty-four; after Marcius, Lucius Tarquinius, called Priscus, thirty-eight; Servius Tullius, who succeeded him, forty-four. And the slayer of Servius, Lucius Tarquinius, the tyrannical prince who, from his contempt of justice, was called Superbus, extended his reign to the twenty-fifth year. 3 As the reigns, therefore, of the kings amount to two hundred and forty-four years or sixty-one Olympiads, it follows necessarily that Romulus, the first ruler of the city, began his reign in the first year of the seventh Olympiad, when Charops at Athens was in the first year of his ten-year term as archon.208 For the count of the years requires this; and that each king reigned the number of years is shown in that treatise of mine to which I have referred."
Olympiad 195, year 1= 1 BC, therefore
Olympiad 92, year 2=412 BC.
Now go back to the first consuls at Rome.
Correcting for Dionysius' 2-year lie, the first consuls of Rome took office on Unius 1, Olympiad 68 year 3. 92-68=24, there were four years per Olympiad, 24*4=96. So the first consuls of Rome took office 94 lunar years before Julian day number 1570570.5. The Roman kings ruled for 244 lunar years, according to Dionysius' sources. 94+244=338.
One 10-month lunar year=295.306 days.
Thus the eclipse happened 338 lunar years before 1570570.5.
338*295.306=99814
1570570.5-99814=1470757.5
The eclipse happened around 1470757.5
Using Fourmilab Calendar Converter you find:
September 12, 687 BC = 1470757.5.
Looking at all the new moons around that time, I found the Julian day number of the eclipse.
Eclipse visible from Rome on Julian day number 1470868.5.
The software says that was 686 BC, but I claimed at the start of the thread that the eclipse took place in 685 BC, how can this be?
The answer is there was a year zero between 1 BC and 1 AD.
PROOF THERE WAS A ZERO BC
To accomplish this proof let's find day one of the Julian calendar under the assumption that Julius Caesar added 89 days to the calendar in 45 BC.
(412-44)*365+89 = 134409
1570570.5 + 134409 = 1704979.5 = Ianuarius 1, 44 BC = day 1 of the Julian calendar
2451544.5 = January 1st, 2000
2451544.5 - 1704979.55 = 746565
746565/365.25= 2043.983
Therefore from day one of the Julian calendar to January 1st 2000, there were 2044 years.
Assume incorrectly that there was no zero BC.
From January 1, 1 AD to January 1, 2000 AD, there were 1999 years. From January 1, 44 BC to January 1, 1 AD there were 44 years. 1999+44=2043. Using Julian day numbers we know that this had to be 2044, therefore there was a 0 BC.
Q.E.D.
QED=quod erat demonstrandum= which was to be demonstrated
Therefore, the solar eclipse that marks the founding date of Rome occurred on Julian day number 1470868.5=Aprilius 1, 685 BC = January 8, 686 BC [Gregorian proleptic], which was to be demonstrated. Q.E.D.
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