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Euclid: Elementa
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On a given finite straight line to construct an equilateral triangle.
lat Clavius p. 35
SVPER data recta linea terminata triangulum æquilaterum constituere.
IN omni problemate duo potissimùm sunt consideranda, constructio illius, quod proponitur, & demonstratio, quâ ostenditur, constructionem rectè esse institutam. Vt quoniam primum hoc problema iubet constituere triangulum æquilaterum super data recta linea terminata quacunque, ita vt linea recta proposita sit vnum latus trianguli. (Tunc enim figura dicitur constitui super recta linea, quando ipsa linea efficitur vnum figuræ latus) idcirco primum oportet construere ex principiis concessis triangulum aliquod, deinde demonstrare, ipsum eâ ratione constructum, esse æquilaterum, hoc est, habere omnia tria latera inter se æqualia. Quod idem in alijs problematibus perspici potest. Hæc etiam duo reperiuntur ferè in omni Theoremate. Sæpenumerò enim vt demonstretur id, quod proponitur, construendum est, atque efficiendum prius aliquid, ceu manifestum erit in sequentibus. Pauca veró admodum sunt theoremata, quæ nullam requirant constructionem.
kin 幾何原本 p.21
於有界直線上。求立平邊三角形。1
Pic431
1. dummy
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