The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Αποτελέσματα 1 - 5 από τα 70.
Σελίδα 11
... vertical or opposite , 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 ...
... vertical or opposite , 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 ...
Σελίδα 12
... vertical angles ; therefore the base AB is equal ( 4. 1. ) to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore ...
... vertical angles ; therefore the base AB is equal ( 4. 1. ) to the base CF , and the triangle AEB to the triangle CEF , and the remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore ...
Σελίδα 40
... vertically opposite : but BDG is a right angle , because it is equal ( 29. 1. ) to the alternate angle DCE ; therefore the remaining angle DGB is half a right angle , and is therefore equal to the angle DBG ; wherefore also the side BD ...
... vertically opposite : but BDG is a right angle , because it is equal ( 29. 1. ) to the alternate angle DCE ; therefore the remaining angle DGB is half a right angle , and is therefore equal to the angle DBG ; wherefore also the side BD ...
Σελίδα 71
... vertical angle of a triangle to construct it in the several cases where the third datum is : - ( a . ) The perpendicular ; ( b . ) The sum of the sides ; ( c . ) The difference of the sides ; ( d . ) One of the angles at the base ...
... vertical angle of a triangle to construct it in the several cases where the third datum is : - ( a . ) The perpendicular ; ( b . ) The sum of the sides ; ( c . ) The difference of the sides ; ( d . ) One of the angles at the base ...
Σελίδα 83
... vertical opposite angles BGA , AGF , FGE ; therefore the six angles EGD , DGC , CGB , BGA , AGF , FGE are equal to one another : But equal angles stand upon equal ( 26. 111 ) circumferences ; therefore the six circumferences AB , BC ...
... vertical opposite angles BGA , AGF , FGE ; therefore the six angles EGD , DGC , CGB , BGA , AGF , FGE are equal to one another : But equal angles stand upon equal ( 26. 111 ) circumferences ; therefore the six circumferences AB , BC ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD axis base bisected called centre circle circumference coincide common cone construction contained coordinate curve described diameter difference dihedral angles direction distance divided double draw drawn edges ellipse equal equal angles equimultiples extremities faces figure formed four fourth given line given point greater hence horizontal inclination intersection join less likewise magnitudes manner meet method multiple opposite parallel parallelogram pass perpendicular perspective picture plane MN plane of projection position preceding prisms problem produced projector Prop proportional PROPOSITION proved ratio reason rectangle remaining respectively right angles SCHOLIUM segment shown sides similar sphere square straight line surface taken tangent THEOR third touch trace transverse triangle triangle ABC trihedral vertex vertical Whence Wherefore whole
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.