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# Title: [Physica, Id Est, Scientia Rerum Corporearum, In Decem Tractatus Distributa] Physica, Id Est, Scientia Rervm Corporearvm, In Decem Tractatvs Distribvta (shelfmarks Leibn. Marg. 7:1-2; ZEN Leibn. Marg. 7:1-2)
# Folio 71, page id 779782283:0157
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PYB. II. DE COMPRESSO EF TErISO.
Tirer, mocu illo concractionis, in AF, quX REdUICREUE IUXFA pEi
chorda imminuitur proportiona
liree, in duobus v. 8. Peomentis a(-
Cumpris, isitur Segmentorum pro-
Porcionalium exeremitares per li-
neam parallelaim Ioventur _cc.
V. 8. TInc duo SeGImCNEA AL, FF,
Eraducta per morum contractionis,
quo se chorda tensa A F sedueic in
AY, ZE, AV, VB, _C. CerIC
cu VeFL, est ad TA, iE2 F. Y, 2d
YA, d BV, ad YA ec. IYV est
Parallela FEB; idem dico de aliis
punetis;isitur omnia puncta chor-
dae cenla moveneur per lineas ic-
ctas parallelas.
DROD. L γ. X X
Fribus modis chordatensa reduci
eis. 4. porest moiu contractionis: nempe
tor modis reducieur; quoc adduci-
EuE, vel cenditur; Ced eribus cen
ditur, per prop. 74. igitur roridem
modis Leduci potest, quod veexem-
Plo explicetur; SIE chorda AB,
Fensa in ABC, S dimitcatur, 2ddu-
cecur in AB, ec Singula puncta con
Trahentur versus A; e hic lc pri-
mus modus reductionis chorda
censae; primo censionis modo res-
Pondens: Secundus modus est, (1
Chorda V p hinc inde cenla, 2d-
duCatur in AC, cum Ce reducat in
: terrius modus est, si chorda.
rensa AC adducta in ADC, vel
II AEC, _C. Le Se reducat in ABC:
obleruentur Cinguli modi, ve de-
inceps s Forre appellari concin-
Bat intelligantur.
PROP. LXZZ
Choraa tensa, inata terrium modum
 primum; in eadem proxoriione
reducitur, quo ad singula chordae ten-
18.81 su Phlttta: Y. 8. it chord AL Feml2
mum modum, punctum F decur-
ric Spatium FL, L vero Sparium IR,
dcC. iTa VE SpatIa SINE VE IOTUIS, MO-
cus vero re dictantiae ab exrremi-
tare A, Per cOrOII. PFOP. 6I. PaCi
modo sc chorda AC, cenla in
AFC, qua reducatue iuxca tertium
modum, punctum P decurrie (pa-
tium PB, C vero spatium IV, R (p 2-
tiu RB, _C. (ed vE F A est ad LA, iF2
FB, est ad IV, Ve constat ex doctri-
na criangulorum proportionaliiun;
igirur chorda censa puncta redu-
cuntur proportionalirer, cum pri-
mo, cum certio modo; lunc enim
reductiones vE motus contractio.
nis; hi rero re spatia aequalibus
temporibus decurla; vides quam
appolice haec inter se convenione.
PROP. LXX XII.
Duando chorda tensa reducitur
inxta primum modum, spatium con-
fectum in linea aequinalet planum: Sic Fig. os
enim chorda AB, centa in AF, e
reducatur primo modo, punctum
F decurrie lineam FI; punctum L,
lineam LK; igitur (I accipianEuE
omnes istae linea Pcortum, a Sinou-
lis punctis chordae censae decurlae,
facient planum criangulare. sir enim
AF longicudo connacuralis praedi- Fis. 55
etae chordae, sirque AB sparium de-
cursum ab extremo illius puncto
mobili A, d CI, decursum ab alio
puncto C; D FI vero, a puncto
D; exc. haud dubie ex his lineis re-
Culeat planum criangulate AF B;
igitur est spacium aquivalens de
cursum in linea, à chorda censa,
quae juxca primum modum se re-
ducito