Barrow, Isaac, 1630-1677, Child, J. M. (James Mark), tr · Chicago, London : The Open court publishing company · leaf 100
cutting GP in L and K; then I assertthat DS : DT = KG : LG For the ratio KG : LGis compounded of KG : GB and GB : LG,that is, of PK : PS and PT : PL,that is, of DB: DS and DT: DB,and hence is equal to the ratio DT : DS. 4.. Let BDT be a triangle, and let any two straight linesBS, BR, drawn through… … [Barrows proof by drawing parallels through L is ratherlong and complicated; the following short proof, using adifferent subsidiary construction, is therefore substituted. Construction.—Draw GXYZ, as in the figures, parallelto TD. Proof.— Since LG : BZ = GX : XZ =: TS : SD, and KG : BZ = GY : YZ =…
Geometry
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![An illustration from Divina proportione : opera a tutti glingegni perspicaci e curiosi necessaria oue ciascun studioso di philosophia: prospettiua pictura sculptura: architectura: musica: e altre mathematice: suavissima: sotile: e admirabile doctrina consequira: e delecterassi: co[n] varie questione de secretissima scientia (1509)](https://img.insideoutlibrary.com/img/200/ia-divinaproportion00paci-131-359.webp)
