The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Página 7
... greater ( 9 Ax . ) than the angle BCD ; therefore the angle ADC is greater also than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal ( Hyp . ) BOOK I. PROP . V. , VI . , VII .
... greater ( 9 Ax . ) than the angle BCD ; therefore the angle ADC is greater also than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal ( Hyp . ) BOOK I. PROP . V. , VI . , VII .
Página 11
... angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB , and CEB to AED . C E B D Because the straight line AE makes BOOK I. PROP . XIII . , XIV . , XV . 11.
... angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB , and CEB to AED . C E B D Because the straight line AE makes BOOK I. PROP . XIII . , XIV . , XV . 11.
Página 15
... the given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . Which was to be done . F 3 E PROPOSITION XXIV . THEOR . If two triangles have two BOOK I. 15 PROP . XXII . , XXIII .
... the given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . Which was to be done . F 3 E PROPOSITION XXIV . THEOR . If two triangles have two BOOK I. 15 PROP . XXII . , XXIII .
Página 21
... which is not a parallelo- gram , the straight line which joins any two of its opposite angles is called a diagonal . opposite sides and angles of the figure are equal to BOOK I. PROP . XXXII . , XXXIII . , XXXIV . 21.
... which is not a parallelo- gram , the straight line which joins any two of its opposite angles is called a diagonal . opposite sides and angles of the figure are equal to BOOK I. PROP . XXXII . , XXXIII . , XXXIV . 21.
Página 25
... , AG ; therefore the triangle ABC is double of the triangle AEC . And the parallelogram FECG is likewise double ( 41. 1. ) of the triangle AEC , because it is upon the same base BOOK I. PROP . XL . , XLI . , XLII . 25.
... , AG ; therefore the triangle ABC is double of the triangle AEC . And the parallelogram FECG is likewise double ( 41. 1. ) of the triangle AEC , because it is upon the same base BOOK I. PROP . XL . , XLI . , XLII . 25.
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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.