The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Página 87
... equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth , if the multiple of the first be less than that of the second , the multiple of the third is also less than that of ...
... equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and fourth , if the multiple of the first be less than that of the second , the multiple of the third is also less than that of ...
Página 89
... Equimultiples of the same , or of equal magnitudes , are equal to one another . 2. Those magnitudes , of which the same or equal magnitudes are equimultiples , are equal to one another . 3. A multiple of a greater magnitude is greater ...
... Equimultiples of the same , or of equal magnitudes , are equal to one another . 2. Those magnitudes , of which the same or equal magnitudes are equimultiples , are equal to one another . 3. A multiple of a greater magnitude is greater ...
Página 90
... equal to E and F together : therefore , whatsoever multiple AB is of E , the same multiple is AB and CD together of E and F together . Therefore , if any magnitudes , how many soever , be equimultiples of as many , each of each ...
... equal to E and F together : therefore , whatsoever multiple AB is of E , the same multiple is AB and CD together of E and F together . Therefore , if any magnitudes , how many soever , be equimultiples of as many , each of each ...
Página 91
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . Let A the first be the same multiple of B the second , that C the third is of D the fourth ; and of A , C , let the equimultiples EF ...
... equimultiples , these shall be equimultiples , the one of the second , and the other of the fourth . Let A the first be the same multiple of B the second , that C the third is of D the fourth ; and of A , C , let the equimultiples EF ...
Página 92
... equimultiples ( Constr . ) whatever of E , F ; and M , N any whatever of G , H as therefore E is to G , so is ( 5 ... equimultiples whatever of the first and third have the same ratio to the second and fourth ; and in like manner , the ...
... equimultiples ( Constr . ) whatever of E , F ; and M , N any whatever of G , H as therefore E is to G , so is ( 5 ... equimultiples whatever of the first and third have the same ratio to the second and fourth ; and in like manner , the ...
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Términos y frases comunes
ABC is equal ABCD angle ABC angle BAC axis bisected centre circle ABC circumference coincide cone conic section construction coordinate planes curve described Descriptive Geometry dicular dihedral angles directrix distance draw edges ellipse equal angles equiangular equimultiples given line given point given straight line greater hence inclination intersection join less Let ABC Let the plane line BC lines drawn magnitudes meet multiple opposite orthograph parabola parallel planes parallelogram parallelopiped perpen perpendicular plane MN plane of projection plane parallel plane PQ prisms profile angles profile plane projecting plane projector Prop Q. E. D. PROPOSITION ratio rectangle rectangle contained rectilineal figure remaining angle respectively right angles SCHOLIUM segment sides six right sphere spherical spherical angle tangent THEOR trace triangle ABC trihedral vertex vertical plane Whence Wherefore
Pasajes populares
Página 19 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Página 35 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Página 4 - AB; but things which are equal to the same are equal to one another...
Página 128 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.* Let AC, CF be equiangular parallelograms, having the angle BCD equal to the angle ECG : the ratio of the parallelogram AC to the parallelogram CF, is the same with the ratio which is compounded of the ratios of their sides. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Página 8 - If two triangles have two sides of the one equal to two sides of the...
Página 36 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced...
Página 21 - BCD, and the other angles to the other angles, (4. 1.) each to each, to which the equal sides are opposite : therefore the angle ACB is equal to the angle CBD ; and because the straight line BC meets the two straight lines AC, BD, and makes the alternate angles ACB, CBD equal to one another, AC is parallel (27. 1 .) to DB ; and it was shown to be equal to it. Therefore straight lines, &c.
Página 65 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles which this line makes with the line touching the circle shall be equal to the angles which are in the alternate segments of the circle.
Página 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Página 116 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.