Cataneo, Girolamo - Hier. Cataneus de arte bellica, sive, de designandis ac construendis arcibus & propugnaculis, necnon & de iis oppugnandis, expugnandis ac propugnandis : de itinere exercitus, ac castrametatione, quando expediat manus cum hoste conserere

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2113 dato, ab eo puncto producere lineam æ qui-
diſtantem ſeu parallelam lineæ datæ.

Sit linea data AB, punctum verò datum extra eam
ſit C, à puncto C ducemus lineam rectam æquidiſtan-
tem lineæ AB hunc in modum: Ducemus a puncto C
lineam rectam in lineam AB, quæ erit linea CE: ſicq́; ha
bebimus angulum CEA. Præterea ſupra lineam AB de-
ſcribemus angulum angulo CEA æqualem, angulum
ſcilicet FGA, idq́; per primam operationem, ſumpto
pro libito in dicta linea AB puncto G: quo facto facie-
mus lineam GF æqualem lineæ EC, per tertiam propo-
ſitionem primi Euclidis: deinde à puncto C ad pun-
ctum F ducemus lineam rectam, quæ erit CF.

20[Figure 20]

Quòd ſi probare velimus lineam CF lineæ AB æqui
diſtantem eſſe, id hoc pacto fiet. Angulus CEA, & an-
gulus FGA æquales ſunt ex ipſa conſtructione: linea
igitur CE æquidiſtans eſt lineæ GF, per primam partem
vigeſimæ octauæ propoſitionis primi Euclidis. Præte-
rea linea GF facta eſt æqualis lineæ CE per conſtructio-
nem: ſicq́; per trigeſimam tertiam primi Euclidis, li-
nea CF æquidiſtans erit lineæ AB, quod erat proban-
dum.

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