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Euclid: Elementa

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4. That all right angles are equal to one another.
lat Clavius p. 24
IV. ITEM quacunque magnitudine data, sumi posse aliam magnitudinem vel maiorem, vel minorem.
OMNIS enim quantitas continua per additionem augeri, per diuisionem vero diminui potest infinitè: Vnde nunquam dabitur quantitas continua adeo magna, quin ea maior dari possit: neque tam parua, quin minor ea possit exhiberi. Hoc idem in numeris verum est, quod ad additionem pertinet. Nam quilibet numerus per continuam additionem vnitatis augeri potest infinitè: quamuis in eius diminutione ad vnitatem indiuiduam deueniatur. 1
1. The fourth postulate of Clavius is not corresponding to the fourth postulate in the earlier versions. The theme of this dictum is rather related to the next paragraph on CUMMVNES NOTIONES. Also the famous parallel postulate is left out by Clavius, see the next record
kin 幾何原本 p.14-15
第四求
(p. 一五)
設一度於此。求作彼度。較此度或大或小。凡言度者。或線或面。或體皆是。或言較小作大可作。較大作小不可作。何者。小之至極。數窮盡故也。此說非是。凡度與數不同。數者。可以長。不可以短。長數無窮。短數有限。如百數減半成五十。減之又減。至一而止。一以下不可損矣。自百以上。增之可至無窮。故曰可長不可短也。度者。可以長。亦可以短。長者增之可至無窮。短者減之亦復無盡。嘗見莊子稱一尺之棰。日取其半。萬世不竭。亦此理也。何者。自有而分。不免為有。若減之可盡。是有化為無也。有化為無。猶可言也。令已分者更復合之。合之又合。仍為尺棰。是始合之初。兩無能幷為一有也。兩無能幷為一有。不可言也
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