Clavius, Christoph - Geometria practica

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7444GEOMETR. PRACT. ſumatur in inſtrumento interuallum inter 10. & 10. æquale, erit interuallum in-
ter 100. & 100. datæ particulæ decuplum.

15. Iam vero ſi viciſsim ex qualibet parte rectæ A B, auferendæ ſint quot-
11Quo modo ex
data linea au-
ferendæ ſint
quotcunque
part{es} decim æ
velaliæ part{es}. cunque decimæ partes vnius, diuidendum erit ſegmentum continens numerum
partium decimarum in 10. pattes æquales. Nam vna pars decima huius ſegmen-
ti continebit decimas partes quæſitas. Vt ſi cupiat quis {7/10}, diuidendum erit
ſegmentum rectæ A B, includens 7. partes, in 10. particulas. Quælibet namq;
harum comprehendet {7/10}. vnius partis rectæ A B. Eademq; ratio eſt de cæteris.
Sed commodius hunc vſum nobis præſtabit inſtrumentum partium ſupra con-
4343[Handwritten note 43] ſtructum. Eius enim beneficio ex quauis recta abſcindemus non ſolum quot-
cunque decimas, ſed etiam centeſimas, decimas nonas, nonageſimas octauas,
& ſic deinceps, vſque ad dimidiatam partem. Nam ſi velimus {3/100}. alicuius
lineæ, capiemus ei lineæ interuallum inter 100. & 100. æquale. Circinus nam-
que extenſus inter 3. & 3. dabit {3/100}. quæſitas. Ita quo que circini pedes inter
50. & 50. dabunt {50/100}. id eſt, {1/2}. Rurſus pedes circini inter 20, & 20. dabunt
{20/100}. hoc eſt, {1/5}. & ſic de cæteris, vt fuſius in vſu prædicti inſtrumenti partium
cap. 1. expoſuimus.

PROBLEMATA VARIA TRIANGV-
lorum rectilineorum.
Capvt III.

TERTIO loco præmiſſuros nos polliciti ſumus varia problema-
ta triangulorum rectilineorum, vt & latera eorum atque anguli
ex quibuſdam datis, & cognitis promptè, atque expeditè, cum id
res poſtulauerit, poſsint erui: quod hoc tertio capite exequemur.
Prioriautem loco de triangulis rectangulis: poſteriori vero de ob-
liquangulis agemus. In margine porrò adſcripſimus propoſitiones noſtri
tractatus triangulorum rectilineorum, in Theodoſio noſtro editi, in quibus
problemata hæc demonſtrantur, vt ſtudioſi intelligant, vnde eorum demon-
ſtrationes, quando libuerit, petere debeant.

TRIANGVLORVM RECTILINEORVM RECTAN-
gulorum problemata.
I. PROPORTIONES LATERVM

Ex datis omnibus angulis cuiuſuis trianguli patefacere.

221. Triang. re-
ctil.

Singulis laterib{us} adſcribantur ſin{us} angulorum oppoſitorum. Latera enim eaſ-
dem proportion{es} habent, quæ inter ſin{us} angulorum laterib{us} oppoſitorum reperiuntur.

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