Sentence Examples


  • We may give in the first place an elementary proof of the converse proposition by the aid of a simple lemma: Lemma.
  • Lemma liii.
  • The lemma is enunciated as follows: " Quaestiones omnes, quae per sinus, tangentes, atque secantes absolvi solent, per solam prosthaphaeresim, id est, per solam additionem, subtractionem, sine laboriosa numerorum multiplicatione divisioneque expedire."
  • Contains also (I), under the head of the de determinate sectione of Apollonius, lemmas which, closely examined, are seen to be cases of the involution of six points; (2) important lemmas on the Porisms of Euclid (see PoRIsM); (3) a lemma upon the Surface Loci of Euclid which states that the locus of a point such that its distance from a given point bears a constant ratio to its distance from a given straight line is a conic, and is followed by proofs that the conic is a parabola, ellipse, or hyperbola according as the constant ratio is equal to, less than or greater than i (the first recorded proofs of the properties, which do not appear in Apollonius).
  • One of the most important rules of the method forms the second lemma of the second book of the Principia.

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