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 páginas |
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... similar solid figures 66 are those which are contained by similar planes of the same number and magnitude . " Now this Proposition is a Theorem , not a Definition ; because the equality of figures of any kind must be demonstrated , and ...
... similar solid figures 66 are those which are contained by similar planes of the same number and magnitude . " Now this Proposition is a Theorem , not a Definition ; because the equality of figures of any kind must be demonstrated , and ...
Página 79
... similar B C a 10.3 . to the segment ADB , and that similar segments of circles contain bequal 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 ...
... similar B C a 10.3 . to the segment ADB , and that similar segments of circles contain bequal 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 ...
Página 81
... BC , EF : But similar segments of cir- cles upon equal straight lines are equal to one another , 24. 3 . therefore the segment BAC is equal to the segment EDF : G C C BOOK III . But the whole circle ABC is equal OF EUCLID . 81.
... BC , EF : But similar segments of cir- cles upon equal straight lines are equal to one another , 24. 3 . therefore the segment BAC is equal to the segment EDF : G C C BOOK III . But the whole circle ABC is equal OF EUCLID . 81.
Página 147
... SIMILAR rectilineal figures are those which have their several angles equal , each to each , and the sides about the equal angles proportionals . 66 II . Book VI . Reciprocal figures , viz . triangles and parallelograms , are See N ...
... SIMILAR rectilineal figures are those which have their several angles equal , each to each , and the sides about the equal angles proportionals . 66 II . Book VI . Reciprocal figures , viz . triangles and parallelograms , are See N ...
Página 158
... similar to the triangle ABC : And the triangles ABD , ACD , being both equiangular and similar to ABC , are equiangular and similar to each other . Therefore , in a right angled , & c . Q. E.D. COR . From this it is manifest that the ...
... similar to the triangle ABC : And the triangles ABD , ACD , being both equiangular and similar to ABC , are equiangular and similar to each other . Therefore , in a right angled , & c . Q. E.D. COR . From this it is manifest that the ...
Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 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...
Página 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.
Página 1 - A straight line is that which lies evenly between its extreme points.
Página 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.
Página 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.
Página 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...