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

### From inside the book

Results 6-10 of 14

Page 25

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**number**of straight lines which may be drawn between an unknown**number**of points being given , required the**number**of ...**multiply**the given**number**of points by the same**number**less 1 , and divide this product by 2 . Between 2 ... Page 26

... number of diagonals which can be drawn in any polygon ? Answer . 1. A triangle can have no diagonal , for the vertex ...

... number of diagonals which can be drawn in any polygon ? Answer . 1. A triangle can have no diagonal , for the vertex ...

**multiply the number**of its sides or angles by the same number less 3 , and divide this pro- duct by 2 . In a ... Page 27

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**number**of diagonals which can be drawn in a polygon to be 35 , how many sides has the polygon ? Answer . This**number**35 is the half of a product found by**multiplying**together two**numbers**, whose dif- ference is 3. We must therefore seek ... Page 35

... number of angles formed at a point is double the number of the concave angles . For as there is a convex wherever ...

... number of angles formed at a point is double the number of the concave angles . For as there is a convex wherever ...

**Multiply the number**of lines by the same number , less 1 . 2 straight lines give 2 x 12 angles . 3 5 66 66 66 66 ... Page 38

... number of triangles . It is 12 3 = 4 . 3. 5 straight lines . If 5 straight lines intersect one another at the ...

... number of triangles . It is 12 3 = 4 . 3. 5 straight lines . If 5 straight lines intersect one another at the ...

**multiply the number**of the lines by the product of the two numbers preceding it in the natural order of the numbers ...### 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.