Select Exercises for Young Proficients in the Mathematics
Select Exercises for Young Proficients in the Mathematics
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In our eReader you can find the full English version of the book. Read Select Exercises for Young Proficients in the Mathematics Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Select Exercises for Young Proficients in the Mathematics
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3.
- '- — BE; CE BE:AE. J^ And, fmce the Ratios of CE and AE to BE are thus given, it follows, that, if any Line FG be drawn parallel to AC, the Parts thereof GH and FH, intercepted by BC, BE, and BA ( produced ) will be to BH in the fame given Ratios, ^, , JAB :CD::BH: GH Or that <[bC: AD::BH:FHf and confequently, that, if BH be taken =:A B, GH will be given z=. CD, and FH= the following Conflruflion.
BC Whence Makr with their Solutions.
i3J Make FH a Fourth-Proportional to BC, AB, and AD (by ...EUm, 13. 5} ; and, in the fame Line produced, take HGzzuCD : Then fby Alg. Lemma on p, 334. ) let a Circle IK be defcribed, fo that two Lines drawn from F and G, to meet any-where in the Periphery Thereof, may obtain the given Ratio of AB to CB. And from H, as a Center, with the Radius AB, let another Arch be defcribed, interfering the Former in B ; draw BF and BG, in which fet off AB and BC of the given Lengths; then, thro' the three Points, A, B, and C, let a Circle be defcribed, and the Thing is done.
What to read after Select Exercises for Young Proficients in the Mathematics?
You can find similar books in the "Read Also" column, or choose other free books by Thomas Simpson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
3.
- '- — BE; CE BE:AE. J^ And, fmce the Ratios of CE and AE to BE are thus given, it follows, that, if any Line FG be drawn parallel to AC, the Parts thereof GH and FH, intercepted by BC, BE, and BA ( produced ) will be to BH in the fame given Ratios, ^, , JAB :CD::BH: GH Or that <[bC: AD::BH:FHf and confequently, that, if BH be taken =:A B, GH will be given z=. CD, and FH= the following Conflruflion.
BC Whence Makr with their Solutions.
i3J Make FH a Fourth-Proportional to BC, AB, and AD (by ...EUm, 13. 5} ; and, in the fame Line produced, take HGzzuCD : Then fby Alg. Lemma on p, 334. ) let a Circle IK be defcribed, fo that two Lines drawn from F and G, to meet any-where in the Periphery Thereof, may obtain the given Ratio of AB to CB. And from H, as a Center, with the Radius AB, let another Arch be defcribed, interfering the Former in B ; draw BF and BG, in which fet off AB and BC of the given Lengths; then, thro' the three Points, A, B, and C, let a Circle be defcribed, and the Thing is done.
What to read after Select Exercises for Young Proficients in the Mathematics?
You can find similar books in the "Read Also" column, or choose other free books by Thomas Simpson to read onlineMoreLess
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