## 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 xviii

... ABC DEF means that the

... ABC DEF means that the

**triangle ABC**is similar to DEF . AB means a square each side of which is equal to the line AB . To avoid the frequent repetition of the term right angle , the abbreviation R. A. is substituted . Thus 2 R. A. is ... Page 60

... TRIANGLES . 70. To construct a triangle which shall be equal to another

... TRIANGLES . 70. To construct a triangle which shall be equal to another

**triangle ABC**, ( fig . 62. ) . 1. Let the 3 sides of ABC be given . Draw a straight line EF equal to one of the given sides , for example , BC . From E as a centre ... Page 61

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**ABC**, to be known . Draw a straight line EF = side BC . At point E make an angle DEF = CBA . Take ED BA , and draw DF . DEF is the**triangle**required . = That the**triangles**thus constructed are in each case equal to the given**triangle**... Page 65

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**triangles**,**ABC**and ADC , but AEFC is composed of 4 triangles , each equal to ABC . 82. Remark . In a right triangle the side opposite to the right angle is called the hypothenuse . Now you will observe that the square constructed upon ... Page 68

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**triangle**, we may construct a regular 6 , 12 , 24 , & c . sided polygon in a circle , and by drawing tangents at the ...**ABC**, ( fig . 63. 2. ) Sol . Bisect the angles A and B by straight lines , which will intersect each other at O. From the ...### 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.