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Euclid: Elementa

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gre I,0
ι῾ Ὅταν δὲ εὐθεῖα ἐπ᾽ εὐθεῖαν σταθεῖσα τὰς ἐφεξῆς γωνίας ἴσας ἀλλήλαις ποιῇ, ὀρθὴ ἑκατέρα τῶν ἴσων γωνιῶν ἐστι, καὶ ἡ ἐφεστηκυῖα εὐθεῖα κάθετος καλεῖται, ἐφ᾽ ἣν ἐφέστηκεν.
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eng
10. When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
lat Sic
Quando autem recta linea stans super rectam eos qui deinceps angulos equales alternis facit, rectus est uterque equalium angulorum, et recta superstans cathetus appellatur in eam cui superstat.
lat Gerard
[x] Quando recta linea super rectam lineam erigitur et fiunt duo anguli ex utraque parte linee erecte equales, tunc unusquisque eorum est rectus; et linea erecta super lineam dicitur perpendicularis super lineam super quam est erecta.
lat Adelard
Quando recta linea supra rectam lineam steterit duoque anguli utrobique fuerint equales, eorum uterque rectus erit, lineaque linee superstans ei cui superstat, perpendicularis vocatur.
lat Hermann
Quando recta linea super rectam lineam steterit duoque anguli utrobique fuerint equales: eorum uterque rectus erit lineaque linee superstans: ei cui superstat perpendicularis vocatur.
ara Uppsala 1v11-13
[١٠] واذا قام خط مستقيم على خط مستقيم فصير ' الزاويتين اللتين عن جنبتيه متساويتين فكل واحدة منهما هي زاوية قائمة ' والخط القائم يقال له عمود على الخط الذي هو قائم عليه
ara Tuṣi p. 3
والقائمة ' من الزوايا هي إحدى المتساويتين الحادثتين عن خنبتي خط مستقيم قام عليه مثله ' ويسمي القائم عمودا
per Shirazi p. 8,8-10
و زاویه قایمه یکی از دو زاویه متساوی باشد کی حادث شده باشند از دو جانب خطی مستقیم کی قایم شده باشد بر مثل خویش و ان خط قایم را عمود خوانند
san 3,17-18
samānarekhāyāṃ lambayogā(18)d utpannau koṇau pratyekaṃ samakoṇau bhavataḥ rekhe ca mitho lambarūpe staḥ |
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lat Clavius p. 9
X. CVM vero recta linea super rectam consistens lineam eos, qui sunt deinceps, angulos æquales intersecerit, rectus est vterque æqualium angulorum: Et quæ insistit recta linea, perpendicularis vocatur eius, cui insistit.
VSVS frequentissimus reperitur in Geometria angulirecti, & lineæ perpendicularis, nec non anguli obtusi, & acuti, propterea docet hoc loco Euclides, quisnam angulus rectilineus apud Geometras appelletur rectus, & quænam linea perpendicularis: In sequentibus autem duabus definitionibus explicabit angulum obtusum, & acutum. Non enim alius dari potest angnlus rectilineus, præter rectum, obtusum, & acutum, Igitur si recta linea A B, rectæ C D, insistens essiciat duos angulos prope punctum B, (qui quidem ideo dicuntur à Maìbematicis esse deinceps, quod eos eadem linea C D, protracta, propo idem punctum B, efficiat) inter se æquales, quod tum demum fiet, quandorecta A B, non magis in C, quam in D, inclinabit, sed æquabiliter rectæ C D, insistet, vocabitur vterque angulus B, rectus, & recta A B, perpendicularis recta C D, cui insistit, Eadem ratione nominabitur recta C B, perpendicularis recta A B: quamuis enim C B, tantum faciat cum A B, vnum angulum, tamen si A B, extenderetur inrectum & continuum versus punctum B, efficeretur alter angulus æqualis priori. Qua vero arte linea duci debeat efficiens cum alter a duos angulos æquales, decebit Euclides propositione 11. & 12. buius primi libri. Itaque vt in Geometria concludamus angulum aliquem esse rectum, aut lineam, quæipsum essicit, ad aliam esse perpendicularem, requiritur, & sufficit, vt probemus angulum, qui est ei deinceps, æqualem illi esse. Pariratione, si dicatur aliquis angulus rectus, aut linea, quæ ipsum constituit, perpendicularis ad aliam, colligere licebit, angulum illi deinceps æqualem quoque esse. Quando enim anguli, qui sunt deinceps, fuerint inter se æquales, nuncupatur vterque illorum rectus, & linea ipsos efficiens, perpendicularis, iuxta banc 10. definitionem: quando autem non fuerint æquales, non dicitur quisquam illorum rectus, vt constabit ex sequentibus duabus definitionibus, & propterea neque linea eos constituens perpendicularis appellatur. Hæc dixerim, vt videas, quidnam liceat ex hac definitione colligere in rebus Geometricis, & quemnam vsum babeant apud Geometr as descriptiones vocabulorum. Non enim magno laborebæc quæ diximus, ad alias definitiones poterunt transferri.
kin 幾何原本 p.5
第十界
直線垂於橫直線之上。若兩角等。必兩成直角。而直線下垂者。謂之橫線之垂線。
量法。常用兩直角。及垂線。垂線加於橫線之上。必不作說角及鈍角。
若甲乙線至丙丁上。則乙之左右作兩角相等。為直角。而甲乙為垂線。
若甲乙為橫線。則丙丁又為甲乙之垂線。何者。丙乙與甲乙相遇。雖止一直角。然甲線若垂下過乙。則丙線上下定成兩直角。所以丙乙亦為甲乙之垂線。如今用矩尺。一縱一橫。互相為直線。互相為垂線。凡直線上有兩角相連是相等者。定俱直角。中間線為垂線。
反用之。若是直角。則兩線定俱是垂線。
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