The geometry, by T. S. Davies. Conic sections, by Stephen FenwickJ. Weale, 1853 |
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Σελίδα 110
... mean term . [ This is sometimes expressed by saying that the arithmetical mean is greater than the geometrical . ] 16. Let any number of pairs of magnitudes have the same ratio : — Also , let any number of the antecedents be combined in ...
... mean term . [ This is sometimes expressed by saying that the arithmetical mean is greater than the geometrical . ] 16. Let any number of pairs of magnitudes have the same ratio : — Also , let any number of the antecedents be combined in ...
Σελίδα 111
... mean ratio , when the whole is to the greater segment as the greater segment is to the less . 4. The altitude of any figure is the straight line drawn from its vertex perpendicular to the base . PROPOSITIONS . PROPOSITION I. THEOR ...
... mean ratio , when the whole is to the greater segment as the greater segment is to the less . 4. The altitude of any figure is the straight line drawn from its vertex perpendicular to the base . PROPOSITIONS . PROPOSITION I. THEOR ...
Σελίδα 119
... mean pro- portional between the segments of the base , and also that each of the sides is a mean proportional between the base , and its segment adjacent to that side : because in the triangles BDA , ADC , BD is to DA , as DA to DC ( 4 ...
... mean pro- portional between the segments of the base , and also that each of the sides is a mean proportional between the base , and its segment adjacent to that side : because in the triangles BDA , ADC , BD is to DA , as DA to DC ( 4 ...
Σελίδα 120
... mean proportional between two given straight lines . Let AB , BC be the two given straight lines ; it is required to find a mean proportional between them . Place AB , BC in a straight line , and upon AC describe the semicircle ADC ...
... mean proportional between two given straight lines . Let AB , BC be the two given straight lines ; it is required to find a mean proportional between them . Place AB , BC in a straight line , and upon AC describe the semicircle ADC ...
Σελίδα 122
... means : and if the rectangle contained by the extremes be equal to the rect- angle contained by the means , the four straight lines are propor- tionals . Let the four straight lines AB , CD , E , F , be proportionals , viz . as AB to CD ...
... means : and if the rectangle contained by the extremes be equal to the rect- angle contained by the means , the four straight lines are propor- tionals . Let the four straight lines AB , CD , E , F , be proportionals , viz . as AB to CD ...
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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.