## An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books |

### From inside the book

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Page xv

... sides of a triangle are divi- ded by a line parallel to the base , such parallel line to the base , • 261. To find a ...

... sides of a triangle are divi- ded by a line parallel to the base , such parallel line to the base , • 261. To find a ...

**homologous sides**of similar triangles , · . 151 Section . 284. Similar polygons are divided by diagonals into ... Page 132

... angles are equal , and a proportion exists between their homolo- gous sides . By

... angles are equal , and a proportion exists between their homolo- gous sides . By

**homologous sides**are meant those which have the same position in the different figures with respect to the equal angles . The angles which are equal in the ... Page 133

Prepared from the Most Approved Prussian Text-books Anna Cabot Lowell.

Prepared from the Most Approved Prussian Text-books Anna Cabot Lowell.

**homologous**, were equal , and other**sides**, not homolo- gous , were proportional . If , for instance , angle A = angle E , angle B = angle G ; or if the proportion ... Page 139

... angles of the one are equal to two angles of the other , each to each . = Dem . Let angle B E , and CF , ( fig ...

... angles of the one are equal to two angles of the other , each to each . = Dem . Let angle B E , and CF , ( fig ...

**homologous sides**of the two triangles are proportional 14 PROPORTIONS . 139 Greater side of a triangle opposite to ... Page 140

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**homologous angles**are equal , the triangles are similar . 265. Two triangles are similar , if the sides of one are proportional to the**homologous sides**of the other , each to each , and the included angles are equal . Dem . ( Fig ...### Other editions - View all

### Common terms and phrases

adjacent angles angle BAC angles are equal Bisect centre chord circumference coincide concave angles consequently angle construct a square convex angle convex surface cube curved line cylinder decagonal describe a circle diagonals diameter divided division points draw a line Draw a straight equal altitude equal angles equal bases equivalent erect a perpendicular exterior angles feet found by multiplying given number given square greatest number hexagon homologous sides hypothenuse inches inscribed circle isosceles triangle length let fall line drawn line passes magnitude measured Multiply the number number of lines number of points number of straight opposite parallelogram parallelopiped passes 2 points pendicular pentagon proportion protractor quadrilateral radii radius equal ratio regular polygon right angle semi-circumference set intersecting side AC similar similar triangles solidity sphere straight line suppose tangents triangle ABC triangular prism unequal vertex vertices

### Popular passages

Page 130 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.

Page 154 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.