The Works of John Playfair Volume 3; On the Arithemetic of Impossible Quantities. on the Causes Which Affect the Accuracy of Barometrical Measurements. Remarks on the Astronomy of the Brahmins. on the Origin and Investigation of Porisms. Observations on (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1822 Excerpt: ... Boscovich's words, is this: ' Problema quo quaeritur recta linea quae quatuor rectas positione datas ita secet, ut tria ejus segmenta sint invicem in ratione data, evadit aliquando in-determinatum, ita ut per quodvis punctum cujusvis ex iis quatuor rectis duci possit recta linea, quae ei conditioni faciat satis." t It is needless, I believe, to remark, that the proposition thus enunciated is a Porism, and that it was discovered by Boscovich, in the same way, in which I have supposed Porisms to have been first discovered by the geometers of antiquity. I shall add here a new analysis of it, conducted according to the method of the preceding examples, and to which the following lemma is subservient. Lemma I. Fig. 15. 32. If two straight lines, AE and BF, be cut by three other straight lines, AB, CD, and EF, given in position, and not all parallel to one another, into segments having the same given ratio, they will intercept between them segments of the lines given in position, viz. AB, CD, EF, which will also have given ratios to one another. Elements, p. 243, Edit. 3. Simpson's solution is remarkably elegant, but no mention is made in it, of the indeterminate case. + Jos. Boscovich Opera, Bassano. Tom. III. p. 331. Demonstration--Through C and E draw CH and EG, both parallel to AB, and let them meet BG, parallel to AE, in H and in G. Let GF and HD be joined; and because AC is to CE, that is, BH to HG as BD to DF, by hypothesis, DH is parallel to GF, and has also a given ratio to it, viz. the ratio of GB to BH, or of EA to AC. Take GK equal to HD, and join EK, and the triangle EGK will be equal to the triangle CHD, and therefore the angle KEG is given, and likewise the angle KEF; and since the ratio of GK to KF is given, if from K there be drawn KL paral...