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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 18C
# Folio 127r, page id 00068193:0255
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n.
2k
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spros
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ano.
Otrat
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De Translatione s. Effectu motus form
lationes sunt ut mobilia.
Sint (Fig.
C
)mobilium AB, CD motus aequidisributi,
longitudines 1A2 A, 1C2C aequales; Ajo trantlationes 1A 2d,
C2D esse ut mobilia. Sit motilium mensura communis Et,
quae trangeratur per longitudinem 1E2E prioribus aequalem;
latet translationem 1E28 ette mensuram translationum
A2B et 1C2C, et toties in illis contineri, quoties EF in mobi-
libus; sunt ergo translationes ut mobilia. Quod si mobilia sint
incommensurabilia, eadem manet ratis per dicta in demonstr. praec
Trop. 3.
Granslationes (vet Effectus formales a motu) sunt in rati-
ne composita mobilium et longitudinum equiditribute
.
percursarum.
Sint (Sig.
)mobilium AB, CD motus aequidittributi
9
per longitudines 1A2 A, 1C3C; Ajo translationes 1A 2B, 1C3D
l
ette inratione compositâ mobilium AB, CD, et longitudinum
102A, 1C3C.
Si essent longitudines aequales, constat per
praecedntem. Si sint maequales, sumatur majoris 1C 3C pars
IC2C aequalis minori 1A2 A, et per 1C2C sit translatio 1C2D.
erit translatio 1A 2B ad translationum 1C2D, ut AB ad Cd
per prop. praec.) Jam translatio 1C2 et ad translationem
L
A
IC3D ut 1C2C (su 1B2B) ett ad 1C3C (per prop. 1. hic). Ergo
7
jungendo prima postremis est translario 1AIB ad translatio-
nem IC3C in ratione componta mobilium AB ad CD, et lon
gitudmum 1B2B ad 1C3C.
In Numeris, si mobilo AB sit ad mobile CD ut 3 ad 3, et
longitudo1A2 AA ad longitudinem 1C3C ut 2 ad 4 (siu 1 ad 2);
erit translatio 1AEB ad translationem 1C3C, ut 6 ad 20 (teu
3 ad 20.)
Prop.
am
a
vel
1A3
es
eo
MMo
Arat