## 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 xii

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**equal**angles are**equal**, . 148. Definition of**equivalent**figures , 149. Altitude of a figure , 150 . 151 . Cases of ...**Radius**may be drawn six times as a chord , 180. To inscribe a regular hexagon , • 181. Approximate ratio of ... Page 10

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**equal**parts , called respectively semi - circles and semi - circum- ferences . A straight line drawn from the centre to any point in the circumference is called a**radius**. Two radii drawn in directly opposite directions form a diameter ... Page 48

... the point of the fixed leg is the centre of the circle . The size of the circle depends upon the greater or less dis- tance between the points of the compasses . The

... the point of the fixed leg is the centre of the circle . The size of the circle depends upon the greater or less dis- tance between the points of the compasses . The

**radius**of the circle is exactly**equal**to this distance : Page 49

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**equal**to this distance : hence , to express the size of a circle , we give the length of its**radius**; thus we say a circle of 1 inch , 1 foot , or 1000 feet**radius**. Many circles may be described , that is drawn , about the same centre ... Page 50

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**radius**of the greater circle passing through the centre of the lesser , as is con- tained between the 2 circumferences . In 6 the distance is exactly**equal**to the difference of the radii . 50. Suppose it is required to draw 10 straight ...### 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.