The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Αποτελέσματα 1 - 5 από τα 74.
Σελίδα 5
... shown , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal ( 1 Ax . ) to one another ; therefore the straight line AL is equal to BC . Wherefore from the given ...
... shown , that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal ( 1 Ax . ) to one another ; therefore the straight line AL is equal to BC . Wherefore from the given ...
Σελίδα 13
... shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , etc. Q. E. D. PROPOSITION XX . B THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ...
... shown that it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , etc. Q. E. D. PROPOSITION XX . B THEOR . Any two sides of a triangle are together greater than the third side . Let ABC be a triangle ...
Σελίδα 14
... shown that BA , AC are greater than BE , EC , much more then are BA , AC greater than BD , DC . Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exterior angle BDC of the ...
... shown that BA , AC are greater than BE , EC , much more then are BA , AC greater than BD , DC . Again , because the exterior angle of a triangle ( 16. 1. ) is greater than the interior and opposite angle , the exterior angle BDC of the ...
Σελίδα 16
... the angle EDF ; B F Neither is it less ; because then the base BC would be less ( 24. 1. ) than the base EF ; but it is not ; therefore the angle BAC is not less than the angle EDF ; and it was shown that 16 EUCLID'S ELEMENTS .
... the angle EDF ; B F Neither is it less ; because then the base BC would be less ( 24. 1. ) than the base EF ; but it is not ; therefore the angle BAC is not less than the angle EDF ; and it was shown that 16 EUCLID'S ELEMENTS .
Σελίδα 17
Royal Military Academy, Woolwich. than the angle EDF ; and it was shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , etc. Q. E. D. PROPOSITION XXVI . THEOR . If two ...
Royal Military Academy, Woolwich. than the angle EDF ; and it was shown that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , etc. Q. E. D. PROPOSITION XXVI . THEOR . If two ...
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Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 4 - AB; but things which are equal to the same are equal to one another...
Σελίδα 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.
Σελίδα 8 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Σελίδα 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.