The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed1855 |
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Side 99
... compounded of two equal ratios . - viz . , the ratio of the first to the second , and the ratio of the second to the third ; hence , it is called duplicate ratio . XI . When four magnitudes are continual proportionals , the first is ...
... compounded of two equal ratios . - viz . , the ratio of the first to the second , and the ratio of the second to the third ; hence , it is called duplicate ratio . XI . When four magnitudes are continual proportionals , the first is ...
Side 120
... compounded of equal ratios , are equal to one another . Let A be to B , as D is to E ; and B to C , as E is to F. The ratio compounded of the ratios of A to B , and of B to C , which ( Def . A ) is the ratio of A to C , is equal to the ...
... compounded of equal ratios , are equal to one another . Let A be to B , as D is to E ; and B to C , as E is to F. The ratio compounded of the ratios of A to B , and of B to C , which ( Def . A ) is the ratio of A to C , is equal to the ...
Side 121
... compounded of several other ratios ; and if one of the first ratios , or the ratio which is compounded of several of them , be equal to one of the last ratios , or to the ratio which is compounded of several of them ; the remaining ...
... compounded of several other ratios ; and if one of the first ratios , or the ratio which is compounded of several of them , be equal to one of the last ratios , or to the ratio which is compounded of several of them ; the remaining ...
Side 122
... compounded of the ratios of h to k , and k to l , which are equal to the remaining first ratios , viz . , of C to D , and E to F. Also , let the ratio of m top , be that which is compounded of the ratios of m to n , n to o , and o to p ...
... compounded of the ratios of h to k , and k to l , which are equal to the remaining first ratios , viz . , of C to D , and E to F. Also , let the ratio of m top , be that which is compounded of the ratios of m to n , n to o , and o to p ...
Side 143
... compounded of the ratios of K to L , and L to M ( V. Def . A ) . Therefore K has to M the ratio compounded of the ratios of the sides . Because BC is to CG , as the parallelogram AC is to the parallelogram CH ( VI . 1 ) . But BC is to ...
... compounded of the ratios of K to L , and L to M ( V. Def . A ) . Therefore K has to M the ratio compounded of the ratios of the sides . Because BC is to CG , as the parallelogram AC is to the parallelogram CH ( VI . 1 ) . But BC is to ...
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The Elements of geometry; or, The first six books, with the eleventh and ... Euclides Uten tilgangsbegrensning - 1881 |
The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle DEF angle EDF base BC bisected centre circle ABC circumference cone cylinder described diagonal diameter draw duplicate ratio equal angles equal Ax equal Const equiangular equimultiples Euclid ex æquali Exercise exterior angle fore given straight line gnomon homologous sides inscribed join less meet multiple opposite angle parallelogram parallelogram AC parallelopiped pentagon perpendicular polygon prism produced proposition Q. E. D. PROP reciprocally proportional rectangle contained rectilineal figure remaining angle right angles segment similar triangles solid angle sphere squares of AC straight line drawn straight lines A B THEOREM third three plane angles three straight lines triangle ABC triangle DEF triplicate ratio twice the rectangle vertex Wherefore whole angle
Populære avsnitt
Side 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 34 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Side 2 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 122 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 135 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Side 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Side 147 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
Side 37 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...