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 the Trigonometrical (Paperback)

This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1822 edition. Excerpt: ...FK, will be equal to that fourth pro portional. But AE' does not intersect FK, for they are parallel by construction; therefore BE' cannot intersect KL; KL is therefore parallel to BE', a line given in position. Again, let AE," BE" be inflected to E," so that AE" may pass through the given point H; then it is plain, that BE" must pass through the point to be found M; for if not, it may be demonstrated, just as has been done above, that AE" does not pass through H, contrary to the supposition. The point to be found is therefore in the line E"B, which is given in position. Now, if from E there be drawn EP parallel to AE', and ES parallel to BE', BS is to SE as BL to LN, and AP to PE as AF to F G; wherefore the ratio of FG to LN is compounded of the ratios of AF to BL, PE to SE, and BS to AP. But the ratio of PE to SE is the same with that of AE' to BE', and the ratio of BS to AP is the same with that of DB to DA, because DB is to BS as DE' to E'E, or as DA to AP. Therefore the ratio of-FG to LN is compounded of the ratios of AF to BL. AE' to BE'. and DB to DA. In like manner, because E" is a point in the line DE, and AE," BE" are inflected to it, the ratio of FH to LM, is compounded of the some ratios of AF to BL, AE' to BE', and DB to DA; and therefore the ratio of FH to LM is the same with that of FG to NL, and the same consequently with that of HG to MN. But the ratio of HG to MN is given, being by supposition that of a to s; the ratio of FH to LM is therefore also given, and FH being given, LM is given in magnitude. NOW, LM is parallel to BE', a line given in position; therefore M is in a line QM parallel...