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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 103, page id 779782283:0189
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LTB. II. DE COMERESSO ET PEHSO.
aneus duo quadeantes, cum du - quadeaEuM E A, ad quadeaCU F. C.
CaNEUE AD, CD, AT, CF, ScC. ita id eR, vc 16. 2d 4. GF, demum ad
VE excesuS LD, NID, sine aequales,
itemque OT, MZ; dico lineam
BDT, elle rectam; CUm CnIM. AD,
CD, Anc aequales, irem AB, BC, item
AT, CT, cerre TB, est perpendicu-
laris, ve constat ex elementis;igitur
punctum adductum B deleribicli-
nea rectam, quod erar demonstrand.
PROP. CL XT.
Si chorda tensa diuidatur inaqua-
lices,  adducatur punctum divisio-
nis, per excessus aequales, describit hy-
15. r4 perbolem: Sic enim cen(a AC, diui
(a II AE, describANEUL ex A, & C,
duo quadrances, (uD Ladiis AF, C F;
cum ductis ex A, _ C, rectis, 2Tu-
mantur verimque exceltus aequales;
V. O. PR, SR; EIIIM FG, LC, eum
THI, RHI; ee per puncta ROFL, du-
cacur linea curua, hec est hyperbo-
lare constat ex conicis: immo de-
Ecribendae hyperbolae es praxis co-
munis: aequi cunc punctum C, addu-
citur per excessus aequales, ex hypo-
cheli; igitur punctum hoc modo
adductum, delcribic hyperbolam.
PROP. CLZII.
Sichorda, cuius viraque extremi-
ras vtrimque immobiliter affixa est,
deorsum incuruerur, format parabo-
6. 13. tam: V. 8. sic Chorda AF, 2fFXA VE
dictum est in A F; SIC parabOla AOP,
dividatur que applicata AE, in par-
res quorliber aequales, v. 8. In 4.
ducanturque quorlibet applicacae
OP, NI, MI, _C. tum demitran-
tur perpendiculares. HD, IC, OD;
dico OF, else ad CM, in carione du-
GO, Ve quadratum F A, 2d quadia-
cum EB, id elt, rE 16. ad 9. itaque (2
OE, SIC 16. HD, exit 15. IC, 12. PB,
7. haec omnia constant ex conicis:
Porro his politis, iam rettac ve de-
monstremus, chordam, cuius vera-
que extremitas in Ceu horizentali
immobilirer aftixa est, propria gr2-
uitaris ri, _ nilu, deortum in p2-
rabolam curuari; quod enim dubi-
tanter cantum alleruie Calileus,
hic demonstrandum est: sic itaque
chorda in Sicu horicontali AZ, Cu-
ius veraque extremitas A, dc Z, im-
mobilicer aftixa sic, deortum haud
dubie grauitat, per prop. 153. CedFis. 165
inaequaliter in omnibus punctis
mediae chorda F A; maxiime veLO
in E; nempe est cenrrum granicaris
cominune: adde quod racio rectis
habenda est, nempe cum F, ita de-
(CendaE, DE CIFCA CCNELUM A, im-
mobile, Cegmencum P. A, deortum
trahat, habet maius inomentum,
Qua C; PUIHE AILLCIL MOICHCA L2-
tione rectis, ve dictantia; v. 9. SIE
E A, dupla CA, mOmenEUIM F, est
duplum momenti C; catione reco
ponderis, momenta lune ve lonoi-
cudines chordarum, igicur rarione
Ponderis, momencum F, est du-
Dlum momenti C, isieur ratione
rectis simul ec ponderis; momen-
CUM F, est quadruplum momenti
C, id est ; VE quadTaTI L A, 2d
quadratum C R; igitus omnia pun-
ctanilii communi concurrune, ad
morum puncti E; quia OA CCHETUMI
commune, de proprer Rexibilicatenr
chorda, omnia puncta AE, CONCUL-
plicata L. A, _ FD; vel ve quadca- eune ad mocum puncti C; quia est
eU EA, ad quadcacum FD, id est,
centrum commune legmenti FA;
F16, 24 1, GL, rer D elle ad GH, rE iremque omnit legmenti AC; adt
MOtM.