An Introduction to Geometry and the Science of Form: Prepared from the Most Approved Prussian Text-books |
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Page xii
... equivalent figures , 149. Altitude of a figure , 150 . 151 . Cases of equivalent parallelograms , 152. A triangle equivalent to half a parallelogram of equal base and altitude , 153. Case of equivalent triangles , 154. Sum of the angles ...
... equivalent figures , 149. Altitude of a figure , 150 . 151 . Cases of equivalent parallelograms , 152. A triangle equivalent to half a parallelogram of equal base and altitude , 153. Case of equivalent triangles , 154. Sum of the angles ...
Page xiii
... equivalent parts , 212. To transform a parallelogram into an equivalent triangle , 213. To construct a square 1 times as great as a given square , 214. To transform a triangle into an equivalent parallelogram , 215. Two diagonals in a ...
... equivalent parts , 212. To transform a parallelogram into an equivalent triangle , 213. To construct a square 1 times as great as a given square , 214. To transform a triangle into an equivalent parallelogram , 215. Two diagonals in a ...
Page xiv
... equivalent to two given squares , " 6 66 equivalent to the sum of 3 , 4 , 5 , or more squares , • 4 , 9 , 16 , & c . times as great as a given . 223 . 224 . " ( 6 225 . 226 . 227 . } Measure of angles formed by two chords , ( 6 • square ...
... equivalent to two given squares , " 6 66 equivalent to the sum of 3 , 4 , 5 , or more squares , • 4 , 9 , 16 , & c . times as great as a given . 223 . 224 . " ( 6 225 . 226 . 227 . } Measure of angles formed by two chords , ( 6 • square ...
Page xvi
... equivalent to two similar given figures , 156 292. Ratio of the parts of intersecting chords , 293. Ratio of the parts of secants , 294. Tangent meeting a secant is a mean proportional between the entire secant and the part without the ...
... equivalent to two similar given figures , 156 292. Ratio of the parts of intersecting chords , 293. Ratio of the parts of secants , 294. Tangent meeting a secant is a mean proportional between the entire secant and the part without the ...
Page 89
... Equivalent figures are such as have equal sur- faces . Two figures may be equivalent , although dis- similar in form ; thus a circle may be equivalent to a square . 149. The altitude of a parallelogram is a line drawn from one side ...
... Equivalent figures are such as have equal sur- faces . Two figures may be equivalent , although dis- similar in form ; thus a circle may be equivalent to a square . 149. The altitude of a parallelogram is a line drawn from one side ...
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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.