Pamela Krantz
). Pamela Krantz
? Except if there are other suggestions?- Section 11 was re-loaded (msg. on bottom page 7) with "quad" changed to "squared" in both places.Rapunzelina wrote:
Section 11:
In (Rq/Iq) × (S cub./D quad.) [02:30] and (Rq × S cub.)/(Iq × D quad.) [03:23] both "q" and "quad." stand for "quadratum". I think it would be better if both were read the same, "squared", as I suggest for Section 9. More clear to the listener and more consistency through the sections.
Pamela KrantzOh boy, here goes:Rapunzelina wrote: I'm a little behind with the sections and I haven't seen Section 17 yet. What kind of difficulty is there? something I can help with?
Pamela KrantzI haven't heard this word pronounced ever, so I can't suggest anything. But if noone has any other idea, "ancients" should be fine.pkrantz wrote: First para. (pg. 169, under Fig. 14): “This was understood by some of the Antients,”
Can we assume this should be pronounced as “ancients”?
This is like another instant in a previous section:pkrantz wrote: Pg. 170, within last sentence of page: “and the Arch QF and Angle AXR will be biggest when ND is to CN as √(II - RR) to √(3)RR, ...”
I'm guessing here -
√(II - RR) - "square root of II (capital pi/product?) minus/to RR"?
√(3)RR - "the third root of RR"?
Have no clue how to read these phrases – you can laugh at my attempts – back in the dark ages, I didn’t have this stuff in school!
So I would suggest something like this:Let the Sine of Incidence out of Glass into Air be as I to R, and out of Water into Air, as K to R, and by consequence out of Glass into Water, as I to K: and let the Diameter of the Sphere to which the convex sides AGD and CHF are ground be D, and the Diameter of the Sphere to which the concave sides BME and BNE, are ground be to D, as the Cube Root of KK—KI to the Cube Root of RK—RI: [...]
Normally I would say that Gr. stands for Gradian (grad or grade), and mathematically a grad equals 360/400 Degrees. But in the text I see the terms Degr. and Gr. used interchangeably, so I don't know what to make of itpkrantz wrote: Pg. 175, near beginning: "8 Gr. 15 Min." - What is “Gr.”?
I would suggest reading "Gr." as "grades". Or do you think it could be an even shorter abbreviation for "Degrees", along with "Degr."? Any other ideas?the greatest Angle AXR will be found 42 Degrees and 2 Minutes, and the least Angle AYS, 50 Degrees and 57 Minutes.
the greatest Angle AXR will be found 40 Degrees and 17 Minutes, and the least Angle AYS 54 Degrees and 7 Minutes.
let POE, POF, POG, POH, be Angles of 40 Degr. 17 Min. 42 Degr. 2 Min. 50 Degr. 57 Min. and 54 Degr. 7 Min. respectively
the Angle SEO being equal to the Angle POE, or 40 Degr. 17 Min.
the Angle SFO being equal to the Angle POF, or 42 Degr. 2 Min.
the Angle SGO being equal to the Angle POG, or 50 Gr. 51 Min.
the Angle SHO being equal to the Angle POH, or 54 Gr. 7 Min.
the Angle POF being 42 Gr. 2 Min. and the least Semi-diameter of the outermost POG, being 50 Gr. 57 Min.
etc.
I think we should go with the original scan here and leave out the second and.Rapunzelina wrote:PL-notes for Section 9
Also, in the same line, the text says "those Lines 3tT, 3pP, and 2tT, and 2pP, and tT, pP, are" but in the original scan it's "those Lines 3tT, 3pP, and 2tT, 2pP, and tT, pP, are".
With a little help from google it turns out that antients is indeed an old spelling of ancients.pkrantz wrote: First para. (pg. 169, under Fig. 14): “This was understood by some of the Antients,”
Can we assume this should be pronounced as “ancients”?
Yes, seems good. But please make a longer pause between "square root of 3" and "times RR", because with correct math notation, only the number is square-rooted, and not the RR value (except for the first equation, where everything is under the root).Rapunzelina wrote: So I would suggest something like this:
√(II - RR) :: square root of II minus RR
√(3)RR :: square root of 3 * RR [: "three RR" or "three times RR"]
√(8)RR :: square root of 8 * RR
√(15)RR :: square root of 15 * RR
√(24)RR :: square root of 24 * RR
It must be degrees, as gradian (or gon over hereRapunzelina wrote:Normally I would say that Gr. stands for Gradian (grad or grade), and mathematically a grad equals 360/400 Degrees. But in the text I see the terms Degr. and Gr. used interchangeably, so I don't know what to make of itpkrantz wrote: Pg. 175, near beginning: "8 Gr. 15 Min." - What is “Gr.”?
I would suggest reading "Gr." as "grades". Or do you think it could be an even shorter abbreviation for "Degrees", along with "Degr."? Any other ideas?
) has been adopted together with the metric system long after Newton's death. If we can assume that this is an "original" version of the book, gradian cannot possibly be meant, unless Newton could see into the future.