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

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

Lapſus grauium in eodem ſegmento Circuli per plures
chordas eſt velocior.

Moueatur graue ex Q in F: Dico velociùs labi per chordas Q
B. BC. CF, quàm per chordas QB. BF. Quia enim velociùs de
ſcendit per duas chordas BC. CF, quàm| per chordam BF per
Theorema tertium: addito motu communi QB, erit velocior
lapſus per QB. BC. CF, quàm per QB. BF.

THEOREMA V.

Pendulum æquali tempore mouetur per arcum Circuli &
chordam eidem ſubtenſam.

Moveatur pendulum TC ex C in B: Dico æquali tempore la
bi per arcum CEB, & chordam CB. Concipiantur enim per ſin
gula puncta CGHIK eiuſdem arcus CEB duci tangentes, &
chordæ his parallelæ BL. BM.BN. BO & c. Quia itaque ex C la
bendo in ſingula momenta mutat inclinationem, quam indu
cunt lineæ tangentes; erit ratio motûs in his homologa motui
per chordas parallelas. Vt ſi labi incipiat per tangentem CD,
interuallum motûs in hac erit æquale motui per chordam pa
rallelam AB. Nullus autem fit motus in CD, verùm immedi
atè transfertur in alias tangentes. Simili modo in GHIK ex
illâ obliquatione contrahetur motus, inſpatia æqualia chordis
parallelis BL. BM. BN, BO: in EPQRS verò æquatur chor
dis BC. BG. BH &c. quæ quidem chordæ ſubten dunt duplum
illius arcûs, cuiús tangens eſt parallela. Eſt enim CEB duplum
arcùs ESB. Atque hæc ratio arcûs dupli, continuatur uſque ad
tangentem BV. quam ubi attigit pendulum ex C, attingit quoque

Page concordance

Text layer

Text normalization

Search

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

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

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