Marci of Kronland, Johannes Marcus, De proportione motus figurarum recti linearum et circuli quadratura ex motu, 1648

Page concordance

< >
Scan Original
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
< >
page |< < of 145 > >|
1les FM, PA. Cùm itaque angulus OMF ſit grad. 33. prim. 30.
ſemiſſis nimirum anguli externi NOM grad. 67: & angulus
OMA grad: 78. prim: 30; quòd æquales ſint arcus AM. FC:
ablato angulo OMF ex OMA, erit angulus reliquus FMA,
hoc eſt illi æqualis FPA grad: 45.
Cùm itaque angulus FIC ſit
quoque oſtenſus grad. 45, erit angulus FIC externus æqualis
angulo interno FPI: quod eſt abſurdum.
THEOREMA III.
Lapſus grauium in ſegmento
Circuli minore, quàm grad: 90. eſt velocior per duas chordas, quàm per
unam chordam.
Moueatur graue ex B in F per arcum grad: 45. Dico veloci­
ùs moueri per duas chordas BC. CF, quàm per unam chordam
BF.
Supponatur BC æqualis CF: & ducatur FQ parallela BC:
in productâ verò BC ſumatur BT æqualis Fque erit itaque BT
partium 11111400, & BC partium 3901806.
Quâ ablatâ ex
BT manet CT partium 7209594.
Adde Logaritmum huius
logaritmo anguli CTH grad. 67. prim. 30; qui per lemma eſt
complementum anguli FCT grad: 22. prim. 30. eritque aggre­
gatum logaritmus lateris CH partium 6659688.
Eſt autem
CH maius latere BC, ſeu CF partium 3901806.
Cùm itaque,
motus ex C in H ſit æqualis duratione motui ex C in T, per pri:
theorema huius; erit mot9 in CF minor duratione motu in CH:
additoque communi motu in BC, motus in BC, CF minor du­
ratione motu in BT ſeu Fque hoc eſt per prop. 15. illi æquali
motu in BF.
THEOREMA IV.

Text layer

  • Dictionary
  • Places

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index