An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books |
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Page xii
... diagonal into 2 equal triangles , 147. In a parallelogram the sides opposite to equal angles are equal , . 148. Definition of equivalent figures , 149. Altitude of a figure , 150 . 151 . Cases of equivalent parallelograms , 152. A ...
... diagonal into 2 equal triangles , 147. In a parallelogram the sides opposite to equal angles are equal , . 148. Definition of equivalent figures , 149. Altitude of a figure , 150 . 151 . Cases of equivalent parallelograms , 152. A ...
Page xiii
... diagonals in a parallelogram bisect each other , 110 110 111 111 112 112 112 113 113 114 114 114 115 · 116 116 . 117 · 117 . 118 . 118 . 118 Section . 216. Two diagonals in a square or lozenge 2 CONTENTS . xiii.
... diagonals in a parallelogram bisect each other , 110 110 111 111 112 112 112 113 113 114 114 114 115 · 116 116 . 117 · 117 . 118 . 118 . 118 Section . 216. Two diagonals in a square or lozenge 2 CONTENTS . xiii.
Page xiv
... Diagonals in a square or lozenge divide the angles into equal . parts ; in other parallelograms into unequal parts ... diagonal of a parallelogram bisects the parallelogram , • · • 220. Ratio of the square of the hypothenuse to the ...
... Diagonals in a square or lozenge divide the angles into equal . parts ; in other parallelograms into unequal parts ... diagonal of a parallelogram bisects the parallelogram , • · • 220. Ratio of the square of the hypothenuse to the ...
Page xv
... the perimeters of similar triangles , 282. Ratio of the surfaces of similar triangles , . 150 • · . 150 283. 66 " homologous sides of similar triangles , · . 151 Section . 284. Similar polygons are divided by diagonals into CONTENTS . XV.
... the perimeters of similar triangles , 282. Ratio of the surfaces of similar triangles , . 150 • · . 150 283. 66 " homologous sides of similar triangles , · . 151 Section . 284. Similar polygons are divided by diagonals into CONTENTS . XV.
Page xvi
... diagonals into similar trian- gles , 285. Formation of similar polygons from similar triangles , 286. Construction of similar figures , 287. To construct a diagram of a field upon a reduced scale , 288. Ratio of the perimeter of similar ...
... diagonals into similar trian- gles , 285. Formation of similar polygons from similar triangles , 286. Construction of similar figures , 287. To construct a diagram of a field upon a reduced scale , 288. Ratio of the perimeter of similar ...
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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.