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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 221, page id 1041163592:0255
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PRINCTPLA MATEIEMATLCA.
quadrata sune ur carundem differentix; _t idcirco cum quadrata ve- L IDEN
locitatum fuerine etiam ut iplarum difterentiae, similis erit amba- Secvrvosi
rum progressio. Ouo demonstrato, consequens est ctiam ut are~
his lineis descripex sine in progrestione consimili cum spatiis quae
velocitatibus describuntur. Ergo s velocitas initio primi tempo-
ris AK exponatur per lineam A B, ex relocitas inicio secundi RL L
per lincam Rk, ec longitudo primo tempore delcripta per aream
KRB; velocirates omnes sublequences exponentur per lineas
subsequentes L.B Mm, ecc. et longirudines dclcripEx per accaS
LLB3 L.m, eEC. HE COMPOSITC, AL LEMPUS EOTuM exPOnatur per Cum-
mam partium Cuarum A M, longitudo eora deleripEA CZPONCTUE PCF
summam partium suarum AMm B. Concipe jam tempus AM ica
dividi in ParECS AR, IL, L M, CEC. UE (InE CA, CR, C L. C M,
ecc. in progressione Geometrica; e crunt partes illae in eadem pro-
gressione, de relocitares AB, IIk, LB M m, ecc. in progrectione ca-
dem inversa, atque spatia descripea AR, KI, L m, _c. xequalia.
d. F. D
Corol. L. PateE erSO quod, sI TeMPUS ExPOnatur Per ACympEOti
partem quamvis AD, e velocicas in principio temporis per ordi.
natim applicatam AB; velocitas in tine temporis expOnetur Der
ordinacam DC, ec spatium torum descriptum per aream HIyper-
bolicam adjacentem ABCD; neenon spatium quod corpus ali-
quod eodem tempore AD, relocitare prima AB, in Medio non
resistente describere pollet, per rectangulum AB X AD.
Corol. 2. Inde datur spatium in Medio relistente descriptum, ca-
Diendo illud ad spatium quod relocitate uniformi B in medionon
resistente simul describi Dossec, uc est arca LIyperbolica ABG D
2d rectangulum ABX AD.
Corol. 2. Datur etiam resistentia Medii, Racuendo eam ipFo mo-
tus inicio equalem esse vi uniformi centripete, quae in cadence cor-
Pore, tempore AC, in Medio non resistente, gencrare Dosset velo-
cieacem AB. Nam si ducatur B Y quae tangat FIyperbolam in B,
EE OCCUErAE AsympEocO in T: recta AT aequalis eric iPM AC, ec
cempus exponet quo relistentia prima unitormiter concnuata colle-
re posset relocitatem toram AB.
Corol 4. De inde dacur eriam proporrio hujus resistentiae adt vim
sravitatis, aliamre quamris datam vim ceneripecam.
COrol. 5. FC vicererla, E datur proporcio relistentix ad datam
quamvis rim centripetam; datur tempus AC, quo vis centripeta
relistentixe requalis generare porsic relocitarem quamvis LB: dc in-
c
22.
WIHHIBBBMHEGIEMBIETHGI MIIIIIIII