Casati, Paolo - Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae

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1quod intercedat diſcrimen inter hanc & dia
trum ſuperiùs inuentam, nil mirum, quią
vbi multiplex diuiſio intercedit, fractiones
aliquæ neglegun

20[Figure 20]
tur, vnde demum
aliqua oritur dif
ferentia.

XXXV
Idem aliter
per Trigo
nometriam.

Sed placeat hìc

vnum prætereą
obſeruare, quo mi
rificè ſum delecta
tus, cum primùm
animaduerti: Do
ctrinam ſcilicet Tri
gonometricam illud idem exhibere poſſę,
quod ab Algebrâ, in ſecundâ methodo indi
catâ, poſt omnes æquationes ſubminiſtra
tur. Fiat enim vt Sinus Verſus comple
menti anguli obſeruati, ad eiuſdem anguli
obſeruati Sinum Rectum, ita nota altitudo
ad aliud, & habebitur quæſita terræ ſemi
diameter. Sit enim CB terræ ſemidiame
ter, BA nota altitudo, AD linea optica tan
gens in D, per quod ex centro C ducatur re
cta CD, quæ producta in E occurrat peri
pheriæ circuli, interuallo CA, ex eodem
centro deſcripti. Eadem ergo eſt Ratio AB
ad BC, quæ eſt ED ad DC. Eſt autem AD

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