# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/779782283:0166
# Permalink to this reading: https://leibnizlegible.com/page/779782283:0166?run=74
# 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 80, page id 779782283:0166
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=779782283&page=166
# Source image: https://digitale-sammlungen.gwlb.de/content/779782283/jpgs/default/00000166.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 87 lines, status machine
# Lines: 87 recognised, mean confidence 0.90
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

PAZSTCAE TR AOTAEES
permutando; peF PrOP. 101. isieur (I
dinerla sic longicudo. Cimul X ten-
LIO, CCIIPOTA CFUNE IN LaLIONC COIM-
Polita ex veraque: r. 8. line chordae
A. B. Chordae R, cenlio, (IC 4. X lon-
gicudo 2. B, vero cenlio, 1. X longi-
tudo L. Sic rario censionum =. aAu-
vacur subduplicata =. PCRmULEEuE
=. Cic racio longicudinum . com-
Donatur veraque . haec est sacio
composita: atque a deo in hoc catu
Tunc aequalia tempora: (I verO Ten-
Sio A lic 4. _ lorisirudo 1. B, vero
censio r. e longicudo 2. (IF Permu-
EaTa LatiO TeNSIONUI . SIE LaciO
Lonsicudinum =. compolita etie=
igitur reductio chorda A, Het Fem-
poic subquadeuplo.
C OR OL L
Ex his collige, quatuor coniu-
rationes; prima dicit eamdem ten-
tionem de longirudinem; secunda,
camdem centionem, led diversam
longicudinem: cecria, camdem lon-
sicudinem, sCd diverlam centionem;
quarta dinerlan censionem, ex lon-
Sicudinem: In pFima, TEIMPOTA LC
ductionum, seu ribTaLIONUI, PUnE
re ipla censiones, de longicudines;
in Pecunda, re iplae longitudines;
in cerria, in carione lubduplicata
censionum, permutando; in quarta,
in ratione composica ex reraque
vltima.
PFXFCFCA (paTIA SUINE CeMPCF VE
eriangula rectangula, sub chorda
non censa, ex excelsu censionis; re-
IOCiTaLES, VeTO exFremOrum pun-
etorum acquisica in ipla reductio-
ne Cune re criangula de quibus su-
xra sib excellibus et chordis.
DROP. CV.
Velocitas acqnisita a rota choraa,
in ipsa reductione, est et cuncus, cu
insbasis est rectangulum, represen-
tans velocitatem acquisitam ab extre-
mo puncto, alcitudo vero ipsa longi-
endo chorda non tensa: Probatur quia
velocicas extremi puncti inicio, est
ad velocicatem alterius, re sparium
a se decurtum, ad spacium ab alio
decurlum; sunt autem haec sparias
re distancia ab exrremo puncto im-
mobili; r. 9. SIc chorda AB, cenla in
AF; sinc duo puncta B, _V; (p2- FIG. L.
tium, quod contrcic F, dum reduci-
TUT, est EI; Spacium vero quod con-
ACiE L, es IR; Sed TR, est ad LI, VF
VB, ad VB; vel VE AT, ad AB; pEa-
cerea relocitas acquisita ab extrC-
mo puncto B, inreductione, est ve
criangulum, Cub spario reductionis,
de relocitare, qua est ivirio per
PrOP. 69. hec aucem est re rensio;
e haec ve centionis excellus; pari
modo relociras acguisica a puncto
V, in reductione chorda AB, est ve
rriangulum (ub eadem alcieudinc et
relocitare puncti V, quae est ad ve-
locicacem puncti B; VE otus ad
mocum; id est, re spatium, ad Spacius
id est, Ve FL, ad TR; vel re distancia,
ad distanciam, id est, VE V A, ad BA;
eum autem B, X V, e alia puncta
chorda, aequali cempore reducan-
tur, relocitas acquisita a B, in Ledu-
ctione, est ad acquisitam, ab V, ve
criangulum eiuldem alcicudinis, 2d
aliud, cujus balis sic ad balim prio-
FiS, VE AV, ad AB; idem dico de aliis
punctis, igieux Si alTUManEuE EOF hu-
eta in chorua Lecuctas Hlaveomu
Colidum, cuius alticudo est ipla lon-
gicudo chorda non cenlee; quod
LEPI
iulmodi eriangula, quor lune pun-