The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth ... Also the Book of Euclid's Data, in Like Manner CorrectedWingrave and Collingwood, 1816 - 528 σελίδες |
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Σελίδα 26
... two other straight lines makes the alternate angles equal to one an- other ... its exterior angle AEF is 16. 1. greater than the interior and opposite ... ever so far , are parallel to one another . AB therefore is parallel to CD .. Wherefore , ...
... two other straight lines makes the alternate angles equal to one an- other ... its exterior angle AEF is 16. 1. greater than the interior and opposite ... ever so far , are parallel to one another . AB therefore is parallel to CD .. Wherefore , ...
Σελίδα 27
... alternate angles AGH , GHD , are equal to one another ; and the exterior angle EGB is equal to the interior and opposite , upon the E same side GHD ; and the two interior angles BGH , GHD upon the same side , are toge- A ther equal to two ...
... alternate angles AGH , GHD , are equal to one another ; and the exterior angle EGB is equal to the interior and opposite , upon the E same side GHD ; and the two interior angles BGH , GHD upon the same side , are toge- A ther equal to two ...
Σελίδα 29
... any triangle be produced , the exterior angle is equal to the two interior and opposite an- gles ; and the three interior angles of every triangle are equal to two right angles . Let ABC be a triangle , and let one of its sides BC be ...
... any triangle be produced , the exterior angle is equal to the two interior and opposite an- gles ; and the three interior angles of every triangle are equal to two right angles . Let ABC be a triangle , and let one of its sides BC be ...
Σελίδα 79
... angles ; the angle ACB is equal to the an- 11. Def . 3 . gle ADB , the exterior to the interior , which is impossible . 16. 1 . Therefore there cannot be two similar segments of a circle upon the same side of the same line , which do ...
... angles ; the angle ACB is equal to the an- 11. Def . 3 . gle ADB , the exterior to the interior , which is impossible . 16. 1 . Therefore there cannot be two similar segments of a circle upon the same side of the same line , which do ...
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is given ABCD AC is equal altitude angle ABC angle BAC base BC bisected Book XI centre circle ABC circumference common logarithm cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC logarithm multiple opposite parallel parallelogram AC perpendicular point F polygon prism proportionals proposition Q.E.D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of BC straight line AB straight line BC tangent THEOR third triangle ABC vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 41 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Σελίδα 180 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 166 - 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 •f the ratios of their sides. DH Let BC, CG be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Σελίδα 2 - A rhomboid, is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles.
Σελίδα 105 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Σελίδα 79 - 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 1 - A straight line is that which lies evenly between its extreme points.
Σελίδα 149 - 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.
Σελίδα 23 - 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 83 - Wherefore from the given circle ABC has been cut off the segment BAC, containing an angle equal to the given angle DQEP PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the...