An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books |
From inside the book
Page xi
... angles according to the nature of their sides , 103. When angles are equal , 104. Adjacent and vertical angles ... exterior angle of a triangle , 125. Value of the three exterior angles of a triangle , 126 . 127 . } Cases of equal ...
... angles according to the nature of their sides , 103. When angles are equal , 104. Adjacent and vertical angles ... exterior angle of a triangle , 125. Value of the three exterior angles of a triangle , 126 . 127 . } Cases of equal ...
Page xii
... angles of a polygon , 155. Value of each angle of a regular polygon , 156. Value of each angle which may be formed at the middle of a polygon by drawing straight lines to its vertices , 157. Value of the exterior angles of a polygon ...
... angles of a polygon , 155. Value of each angle of a regular polygon , 156. Value of each angle which may be formed at the middle of a polygon by drawing straight lines to its vertices , 157. Value of the exterior angles of a polygon ...
Page 46
... Angles . Triangular pyramid has quadrangular pentagonal 66 66 4 + 1 5 3 + 1 = 4 = ፡፡ 66 decagonal 66 66 5 + 1 6 10 + 1 = 11 46. We will now find by calculation the number of lines and angles in the regular solids . I. Lines . 1. Exterior ...
... Angles . Triangular pyramid has quadrangular pentagonal 66 66 4 + 1 5 3 + 1 = 4 = ፡፡ 66 decagonal 66 66 5 + 1 6 10 + 1 = 11 46. We will now find by calculation the number of lines and angles in the regular solids . I. Lines . 1. Exterior ...
Page 54
... exterior parallels , with a radius equal to the distance between the first ... exterior arcs IK , KH , ' HG , and GI , is formed a connected figure called an ... ANGLES . 59. Before proceeding to the construction 54 CONSTRUCTION .
... exterior parallels , with a radius equal to the distance between the first ... exterior arcs IK , KH , ' HG , and GI , is formed a connected figure called an ... ANGLES . 59. Before proceeding to the construction 54 CONSTRUCTION .
Page 76
... exterior angles upon the same side . A and E , B and F , G and C , H and D , are external internal angles , because one is without and the other within the parallels , and both are on the same side of the single line . We have also many ...
... exterior angles upon the same side . A and E , B and F , G and C , H and D , are external internal angles , because one is without and the other within the parallels , and both are on the same side of the single line . We have also many ...
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.