Elements of Geometry: Containing the First Six Books of Euclid with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added, Elements of Plane and Spherical TrigonometryJ.P. Lippincott & Company, 1855 - 318 σελίδες |
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Αποτελέσματα 1 - 5 από τα 60.
Σελίδα 9
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . 14. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . 15 ...
... diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . 14. A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter . 15 ...
Σελίδα 33
... diameter is a straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the oppo- site sides and angles of the figure are equal to one another ; and the diam- eter BC bisects it . A B D ...
... diameter is a straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter ; the oppo- site sides and angles of the figure are equal to one another ; and the diam- eter BC bisects it . A B D ...
Σελίδα 35
... diameter AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it ; and the halves of equal things are equal ( 7 . Ax . ) ; therefore the triangle ABC is equal to the ...
... diameter AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it ; and the halves of equal things are equal ( 7 . Ax . ) ; therefore the triangle ABC is equal to the ...
Σελίδα 36
... is double ( 34. 1. ) of the triangle ABC , because the diameter AC divides it A B D E C into two equal parts ; wherefore ABCD is also double of the triangle EBC PROP . XLII . PROB . To describe a parallelogram 36 ELEMENTS.
... is double ( 34. 1. ) of the triangle ABC , because the diameter AC divides it A B D E C into two equal parts ; wherefore ABCD is also double of the triangle EBC PROP . XLII . PROB . To describe a parallelogram 36 ELEMENTS.
Σελίδα 37
... diameter of any parallelogram , are equal to one another . Let ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other ...
... diameter of any parallelogram , are equal to one another . Let ABCD be a parallelogram of which the diameter is AC ; let EH , FG be the parallelograms about AC , that is , through which AC passes , and let BK , KD be the other ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder definition demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC line BC magnitudes meet opposite angle parallel parallelogram parallelopiped perpendicular plane polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore
Δημοφιλή αποσπάσματα
Σελίδα 41 - 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 of the line between the points of section, is equal to the square of half the line.
Σελίδα 70 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 45 - Again, because the angle at B is half a right angle, and FDB a right angle, for it is equal...
Σελίδα 91 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 273 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 25 - Parallelograms upon the same base and between the same parallels, are equal to one another.
Σελίδα 130 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Σελίδα 61 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...