## 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 xi

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**Proportions**which may be demonstrated by erecting a perpen- dicular on the middle of the base of an isosceles triangle , 134. The sides of a triangle which are opposite to equal angles are equal , 135. Case of equal right - angled ... Page xv

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**PROPORTIONS**. 246. Meaning of terms ratio ;**proportion**; geometrical**proportion**; antecedent ; consequent ; extremes ; means ; mean propor- tional , 247. Test of**proportion**, 248. Formation of new**proportions**, 249. When figures are ... Page 93

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**proportion**. The size of each exterior angle of a polygon may be found by dividing 4 R. A. by the number of sides in the polygon . each exterior angle of a triangle = R. A. = 120 ° ፡፡ 66 Thus pentagon R. A. 72 ° & c . = = 345 SO TABLE ... Page 130

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**PROPORTIONS**. 1. OF GEOMETRICAL**PROPORTIONS**IN GENEral . 246. The term ratio is used to denote the compara- tive ...**proportion**. For example , ( fig . 142 ; ) in the triangles ABC and DEF , let DE 2 AB , and DF 2 AC , and EF2 BC ... Page 131

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**proportion**is the equality of ratios ; hence two or more ratios are required to form a**proportion**. Propor- tion does not require the equality of the quantities , but the equality of the ratios ; hence two lines may form a**proportion**...### 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.