I was reading this interesting post about Ptolemy’s directions, an example which always makes me crazy for its difficulty, it’s because numbers confuse me, and the example is very difficult.
So let’s try to make some order, (I’m a Virgo Sun). We should calculate the arc of direction between A and B.
Right Ascension 44.59′
A: point A (0 Aries)
Right ascension 0, declination 0, temporal hours 15, hour distance 2,9989
B: point B (0 Gemini)
Right ascension 57.46′, declination 20N21, temporal hours 17.1635, hour distance 0.7448
Meridian distance, i.e. distance from MC = RA MC – RA B = 57.46′-44.59’= 12.47′ —-> 12.78 (decimals)
MD: Meridian Distance
HD: Hourly Distance
TH: Temporal Hour
This is the formula used:
Direction Arc = MD b + HD a * TH b
In Ptolemy’s example, as read in the mentioned post:
12.78 + 2.9989 * 17.1635 = 12.78 + 51.47 =64. 25 —> 64.15’
but we can make the same in a more elegant and easy way, as just Italian girls can do 🙂 Italian girls have their ways, very different from the rest of the world.
In fact why we should multiply hour distance of A for temporal hour of B? It’s occult for a poor girl.
But we can do better, isn’it?
Direction Arc = (DH b + DH a ) * TH b
in fact :
( 0.7448 + 2.9989 ) * 17.1635 = 3.7437 * 17.1635 = 64.25 –> 64.15’
In fact we are just calculating the distance (in hours) that the point B should travel in order to arrive to point A, and then we should multiply this distance for its temporal hours.
In this case the distance which B should travel is 3.7437 because it ‘s distant 0,7448 from MC and then it should move from MC to A of 2.9989 . We already know its temporal hours, which are 17.1635. So we can multiply these two data. Easier. At least for me, I don’t know for Ptolemy.
No magic! It’s just the same formula, after some math passages.
Let’s take in fact our formula
(DH b + DH a ) * TH b,
now we should consider that:
HD= MD/TH from this
MD= HD * TH
so our formula will become:
MDb + DHa*THb
exactly rough Ptolemy’s method 🙂
Before closing the post, I should mention that Italians always distrust Latin quotes.
We call it Latinorum. It’s because our education, this is from one of our most famous texts, Manzoni’s Betrothed.
`Do you know what the number of absolute impediments is?`
`What would you have me know about impediments, sir?`
`Error, conditio, votum, cognatio, crimen, cultus disparitas, vis, ordo . . . Si sit affinis . . .`
`Are you making game of me, sir? What do you expect me to know about your latinorum?`
`Then, if you don`t understand things, have patience, and leave them to those who do.`
Manzoni uses the wrong case, Latinorum, because it is wrong – in fact it is the genitive plural – but especially because it’s more sophisticated to the ears of poor workers. In the story in fact Renzo and Lucia went to the lawyer to have justice, and they found just a complice of the wicked Don Rodrigo, who used Latin just to confuse and cheat poorer and weaker people.
Anyway Manzoni gives us some hope: in fact near the lawyer Quibble-weaver who uses his books more for scenery than for some utility there is Fra Cristoforo, the monk who uses Latin as a precious tool in order to comfort and console, but he shows his good intentions with facts and active friendship.
Marco Fumagalli: I moti del Cielo