Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 páginas |
Dentro del libro
Resultados 1-5 de 17
Página 128
... multiple ; and that which measures the other , its sub- multiple . 5. Like multiples and submultiples are those which contain their measures equally , or which equally measure their corresponding compounds . 6. Quantities are ...
... multiple ; and that which measures the other , its sub- multiple . 5. Like multiples and submultiples are those which contain their measures equally , or which equally measure their corresponding compounds . 6. Quantities are ...
Página 134
... might be extended to the products of any multitude of numbers . PROP . III . THEOR . Homogeneous quantities are proportional to their like multiples or submultiples . Let A , B be two quantities of the same 134 ELEMENTS OF GEOMETRY .
... might be extended to the products of any multitude of numbers . PROP . III . THEOR . Homogeneous quantities are proportional to their like multiples or submultiples . Let A , B be two quantities of the same 134 ELEMENTS OF GEOMETRY .
Página 135
... multiples ; then A : B :: pA : pB . For , since A and B are capable of being measured to any required degree of precision , suppose a to be the mea- sure which A and B contain m and n times , or that A m.a and Bn.a ; consequently pA = p ...
... multiples ; then A : B :: pA : pB . For , since A and B are capable of being measured to any required degree of precision , suppose a to be the mea- sure which A and B contain m and n times , or that A m.a and Bn.a ; consequently pA = p ...
Página 136
... multiple or submultiple of the second , the third is a like multiple or submultiple of the fourth . Let A B C : D ; if A = pB , then C = pD . For , suppose the approximate measures of A and C to be a and c , and let Amp.a , and C = mp.c ...
... multiple or submultiple of the second , the third is a like multiple or submultiple of the fourth . Let A B C : D ; if A = pB , then C = pD . For , suppose the approximate measures of A and C to be a and c , and let Amp.a , and C = mp.c ...
Página 150
... multiple ; and since it also measures A , it must mea- sure the difference between the multiple of B and A ( V. 1. cor . 1. ) , that is , C ; the required measure , there- fore , measures the multiple of C , and consequently the ...
... multiple ; and since it also measures A , it must mea- sure the difference between the multiple of B and A ( V. 1. cor . 1. ) , that is , C ; the required measure , there- fore , measures the multiple of C , and consequently the ...
Contenido
199 | |
200 | |
204 | |
224 | |
225 | |
226 | |
256 | |
257 | |
73 | |
92 | |
95 | |
101 | |
110 | |
125 | |
128 | |
155 | |
181 | |
260 | |
262 | |
264 | |
283 | |
318 | |
338 | |
365 | |
Otras ediciones - Ver todas
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sine square of AC squares of AB straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
Pasajes populares
Página 30 - ... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Página 333 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when any...
Página 294 - If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles...
Página 10 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 137 - Componendo, by composition ; when there are four proportionals, and it is inferred that the first together with the second, is to the second, as the third together with the fourth, is to the fourth.
Página 84 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.
Página 292 - Thus, for" example, he to whom the geometrical proposition, that the angles of a triangle are together equal to two right angles...
Página 93 - UPON a given straight line to describe a segment of a circle containing an angle equal to a given rectilineal angle.
Página 38 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 58 - The rectangle contained by the sum and difference of two straight lines is equivalent to the difference of the squares of these lines.