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. 1903 Excerpt: ...any translation of the group not parallel to T%. Let T' be represented in magnitude and direction by 05, = 2t2. Along OBl take a ' row' of points... B-., O, B1, B2, B3, ... of interval OB1, through them draw parallels to OA, and through...A-2, A-1, O, A1, A2, A3, ... draw parallels to 05, . These two ' sets' of lines ...
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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. 1903 Excerpt: ...any translation of the group not parallel to T%. Let T' be represented in magnitude and direction by 05, = 2t2. Along OBl take a ' row' of points... B-., O, B1, B2, B3, ... of interval OB1, through them draw parallels to OA, and through...A-2, A-1, O, A1, A2, A3, ... draw parallels to 05, . These two ' sets' of lines meet at the points of a net (Fig. 65). Let E be any point of this net, then OE represents a translation of the group; for if E be the intersection of the line through A parallel to OB, and the line through Bn parallel to OA, y OE represents the resultant of the translations OAm and AmE, i. e. of OAm and OBn (since two parallel and equal lines represent the same translation), i.e. of 2mr1 and 2%r2. There are no translations of the group parallel to the plane OA1B1 other than those represented by lines such as OE. For suppose there could be such a translation 0F, where V lies in (or on the perimeter of ) the parallelogram p formed If the point A0 is supposed to coincide with 0, this will cover all possible cases; n being zero or any positive or negative integer. f The 2 is inserted to avoid fractions later. j 2" may be equal to T, but must not be smaller. $ 'The translation OV means 'the translation represented in magnitude and direction by OV, ' and so throughout the book. I But not at a vertex of p. by the lines through Am_1 and Am parallel to OB1 and the lines through and B parallel to OAr Then combining the translation O V with the translations T1-"1 and J"1-" we see that there must be a point F situated with respect to OA1DB1 in the same way that V is situated with respect to p, and such that OF is a translation of the group. In this case the lines FAU FD, FB1 would also represent translations of the group, and...
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New. Sewn binding. Cloth over boards. 280 p. In Stock. 100% Money Back Guarantee. Brand New, Perfect Condition, allow 4-14 business days for standard shipping. To Alaska, Hawaii, U.S. protectorate, P.O. box, and APO/FPO addresses allow 4-28 business days for Standard shipping. No expedited shipping. All orders placed with expedited shipping will be cancelled. Over 3, 000, 000 happy customers.
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