DelMonte, Guidubaldo - Mechanicorvm Liber

121

PROPOSITIO I.

Cuneus hoc modo circa cylindrum accommo
datus, nihil eſt aliud; niſi cochlea duas habens he
lices in vnico puncto inuicem coniunctas.

232[Figure 232]

Sit cuneus ABC; & AB
ipſi BC æqualis. diuidatur
AC bifariam in D, iunga
turq; BD; erit BD ipſi AC
perpendicularis; & AD
ipſi DC æqualis, triangu
lumq; ABD triangulo C
BD æquale. fiant deinde
triangula rectangula EFG
HIk non ſolum inter ſe,
verùm etiam vtriq; ADB
& CDB æqualia. ſitq; cy
lindrus LMNO, cuius perimeter ſit æqualis vtriq; FG kI. &
LMNO ſit parallelogrammum per axem. fiatq; MP æqualis
FE; & PN æqualis HI. ponaturq; HI in NP, circumuolua
turq; triangulum HIk circa cylindrum; & ſecundùm kH helix
deſcribatur NQP, vt Pappus quoq; docet in octauo libro propo
ſitione vigeſima quarta. ſimiliter ponatur EF in MP, circum
uoluaturq; triangulum EFG circa cylindrum; deſcribaturq; per
EG helix PRM. cùm itaq; PMPN ſint æquales EFHI, erit
MN æqualis ipſi AC, & cùm helices PRM PQN ſint æquales
lineis EGHk; helices igitur ipſis ABBC æquales erunt. cu
neus ergo ABC totus circumuolutus erit circa cylindrum LMNO.

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