. Asiatic researches, or, Transactions of the Society instituted in Bengal for inquiring into the history and antiquities, the arts, sciences and literature of Asia. If two rlo'lit lines, a e, do, stand upon a riglit Vint a (I, so that the two internal an- _r,ies e a d, o d b are a bed less tlian two riglit angles, the lines a e, do, produced on the same s,de of ab, shall meet. N. B. This is the liith axiom of the 1st book of Euclid. 1st. Let one of the lines, a e, be perpendicular to ad, and consequently the angle id a acute (bv sup- position) from any point .r, in the line d i, let fall a pe
. Asiatic researches, or, Transactions of the Society instituted in Bengal for inquiring into the history and antiquities, the arts, sciences and literature of Asia. If two rlo'lit lines, a e, do, stand upon a riglit Vint a (I, so that the two internal an- _r,ies e a d, o d b are a bed less tlian two riglit angles, the lines a e, do, produced on the same s,de of ab, shall meet. N. B. This is the liith axiom of the 1st book of Euclid. 1st. Let one of the lines, a e, be perpendicular to ad, and consequently the angle id a acute (bv sup- position) from any point .r, in the line d i, let fall a perpendicular .v c, meeting ad in c; take xo zi d,v; produce ; draw the perpendiculars o^, on. Now in the triangles oxu^dxc, the angles at .v are vertical, and those at u and c right angles, and the siVie equal to .vd, icd — on. (25. \.) — bc (prop, ad.) therefore, if from the line da be taken equal to cd, till the whole be exhausted, and from d i pro- duced be taken the same number of parts =: to da:, and right lines be drawn from the several points of divi- sion in di to the corresponding points of division in ad, these lines will be all perpendicular Xoaa, but tiie last of them either coincides with ae or fails beyond it: di must meet ae. Fig. If both the lines a e, di form acute angles Avith a d, erect the per- pendicular r/???.- by the last ca e 4 l must meet d am, atid tbei etore must first meet a e^ G G Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Asiatic Society (Calcutta, India). London : [s. n. ]
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