d. mo„ T PHILOSOPHIC n a t u r a l i s
c“ '“ “ Sm m a Bl' c i ; m,.l,T " " 0,"ounro a , a, c , D, E, F continume proport’iIo’1n0a1 le&s • «&r■a liìn um Hua™m.
- B ? b . T “ a rE" qUOranl - u n i ’ i „ t r‘ ff ' " tr i e? i
dum eit de lateribu, reftanguli cnjnfcunque d f
Scholium.
eandem eife cum methodo Sluiii tnm a 1Um ^uam PufpiC£>bar
junsi: H H communicata; fab.
H B WUMM M W W S B B
chan teas vel quomodocunaue re Et at l',*,*,* /• r five meu
., M L . *j r , r Z « Z l J Z 7/ ; f™ m: r ’
ra de curvslatibus, arsis, hnmudinibus ^ B P I ? r0!>lett(*tum d M-
ß n t immrn,,.
de his rebus f c r i p f e j . M e . S V h T “' " ” BBti '<7‘
turn coniinetur in iemmate precedente. SCK'
PROPOSITIO Vili. THEOREMA VI
I B H B H H B B ^ H ^ B H
pfarTt,urTn, (MaddefndTo „ß j} e „ ,m ' "miUaeii aJ ^ ;m ;
quando corpus afeendh, vd ip/am f o n d , corpus
P R I N C I P I A M A T H E M A T I C A . 247
pus defcendit) invefìigentur vires abfoluta ,• dico quod vires S^c'™*vs
ilia abfoluta funt inprogrejfione geometrica.
Exponatur enim vis gravitatis per datam lineam A C -, refiftentia
per lineam indefinitam A K ; vis abfoluta in defcenfu corporis per
differentiam K C -, velocitas corporis per lineam A T , q.uee lit media
proportiönalis inter A K & A C , ideoque in fubduplicata, radone
reiiitentise ; incrementum refiftentis data temporis particula fa cium
per lineolam K L , & contemporaneum velocitatis incrementum per
lineolam T <pj & centro C afymptotis redangulis C A, CH defcri-
batur hyperbola quaevis BNS , ereftis perpendiculis A B , KN, LO
occurrens in B, N, O. Quoniam A K eit ut A T q, erit hujus mo.
mentum K L ut illius momen- h
“ m V i P g . i d e f t , ut A P ¡11
KC-, nam velocitatis incrementum
?>|>,(per motus leg. 11.)
proportionale eft vi generanti
KC. Componatur ratio ipfius K B
cum ratione ipfius KN , & fiet
redangulum K L x K N ut A T c rip l k i
x K C x K N ; hoc eft, ob datum redangulum K C x K N , ut A T .
Atqui arem hyperbolicac K N O L ad redangulum K L x K N ratio
ultima, ubi coeunt punda K & L , eft cequalitatis. Ergo area ilk
hyperbolica evanefcens eft ut A T . Componitur igitur area tota hyperbolica
A B O L ex particulis K N O L velocitati A T femper
proportionalibus,.. & propterea fpatio velocitate ifta defcripto pro-
portionalis eft. Dividatur jam area ilia in partes suquales A B MI ,
IMNK, K N O L , &c. & vires abfolutae AC, IC, KC, L C , &c.
erunt in progreffione geometrica. ^ E. T>. Ejt fimili argumento,
in afcenfu corporis, fumendo, ad contrariam partem pundi A, x-
quales areas A B mi, imnk, knot, & c. conftabit quod vires abfo-
lutse A C , iC, kC, 1C, &c. funt continue proportionales. Ideoque ft
fpatia omnia in afcenfu & defcenfu capiantur aequalia ; omnes vires
abfolutce 1C, kC, iC, AC, 1 C, KC, LC, &c. erunt continue proportionales.
E. T).
Carol, i . Hinc ft fpatium defcriptum exponatur per aream hyper-
bolicam A B N K ; exponi poftunt vis gravitatis, velocitas corporis
• & re