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
... homologous terms , -that is , terms which agree with one another as to their name ; and the second and the fourth being the consequents of the two ratios , are also called homologous terms . " Geometers make use of the following ...
... homologous terms , -that is , terms which agree with one another as to their name ; and the second and the fourth being the consequents of the two ratios , are also called homologous terms . " Geometers make use of the following ...
Side 125
... homologous ; and conversely , if the two sides , or these sides produced , be cut proportionally , so that the segments between the base and the parallel are homologous , the straight line which joins the points of section is parallel ...
... homologous ; and conversely , if the two sides , or these sides produced , be cut proportionally , so that the segments between the base and the parallel are homologous , the straight line which joins the points of section is parallel ...
Side 126
... homologous , are parallel . Exercise 1 - If a straight line be drawn parallel to the base and cutting the sides of of a triangle , these sides are proportional to the segments cut off each of them respectively ; and in the two triangle ...
... homologous , are parallel . Exercise 1 - If a straight line be drawn parallel to the base and cutting the sides of of a triangle , these sides are proportional to the segments cut off each of them respectively ; and in the two triangle ...
Side 128
... homologous sides , that is , are the antecedents or consequents of the ratios . F Let A B C and DCE be equiangular triangles , having the angle ABC equal to the angle DCE , and the angle A CB to the angle DEC ; and consequently the ...
... homologous sides , that is , are the antecedents or consequents of the ratios . F Let A B C and DCE be equiangular triangles , having the angle ABC equal to the angle DCE , and the angle A CB to the angle DEC ; and consequently the ...
Side 129
... homologous sides . Let the triangles A B C and DEF have their sides proportionals , sɔ that A B is to B C , as D E to EF ; and BC is to CA , as EF to FD ; and therefore , ex æquali , B A is to A C , as ED is to DF . The triangle ABC is ...
... homologous sides . Let the triangles A B C and DEF have their sides proportionals , sɔ that A B is to B C , as D E to EF ; and BC is to CA , as EF to FD ; and therefore , ex æquali , B A is to A C , as ED is to DF . The triangle ABC is ...
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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...