Newton, Isaac - Philosophia naturalis principia mathematica

Scan	Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80

Scholium.

Et ſimili argumento corpus movebitur in Ellipſi vel etiam in
Hyperbola vel Parabola, vi centripeta quæ ſit reciproce ut cu
bus ordinatim applicatæ ad centrum virium maxime longinquum
tendentis.

PROPOSITIO IX. PROBLEMA IV.

Gyretur corpus in SpiraliPQS ſecante radios omnesSP, SQ, &c.

19[Figure 19]
in angulo dato: requiritur Lex
vis centripetæ tendentis ad
centrum Spiralis.

Detur angulus indefinite par
vus PSQ,& ob datos omnes
angulos dabitur ſpecie figura SPQRT.Ergo datur ratio (QT/QR), eſtque
(QT quad./QR) ut QT,hoc eſt ut SP.Mutetur jam uteunque angulus PSQ,
& recta QRangulum contactus QPRſubtendens mutabitur (per
Lemma XI.) in duplicata ratione ipſius PRvel QT.Ergo manebit
(QT quad./QR) eadem quæ prius, hoc eſt ut SP.Quare (QTq.XSPq/QR)
eſt ut SP cub.adeoque (per Corol. 1 & 5 Prop. VI.) vis centripeta eſt
reciproce ut cubus diſtantiæ SP. que E. I.

Idem aliter.

Perpendiculum SYin tangentem demiſſum, & circuli Spiralem
tangentis chorda PVſunt ad altitudinem SPin datis rationibus;
ideoque SP cub.eſt ut SYqXPV,hoc eſt (per Corol. 3 & 5 Prop.VI.)
reciproce ut vis centripeta.

LEMMA XII.

Parallelogramma omnia, circa datæ Ellipſeos vel Hyperbolæ diametros
quaſvis conjugatas deſcripta, eſſe inter ſe æqualia.

Conſtat ex Conicis.

Page concordance

Text layer

Text normalization

Search

Scan	Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80

Scan	Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80

Scan	Original
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80