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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Σελίδα 13
... base BC be equal to the base EF ; and the tri- angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to ...
... base BC be equal to the base EF ; and the tri- angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to ...
Σελίδα 14
... base BC shall coincide with the base EF cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ...
... base BC shall coincide with the base EF cor . def . 3. ) , and shall be equal to it . Therefore also the whole triangle ABC shall coincide with the whole triangle DEF , so that the spaces which they contain or their areas are equal ...
Σελίδα 15
... base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the ... BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is ...
... base of the triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the ... BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is ...
Σελίδα 16
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... BC equal to the base EF . The angle BAC is equal to ' he angle EDF . For , if the triangle ABC be applied to the ...
... base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle ... BC equal to the base EF . The angle BAC is equal to ' he angle EDF . For , if the triangle ABC be applied to the ...
Σελίδα 17
... base BC coincides with the base EF , the sides BA , AC cannot but coincide with the sides ED , DF ; wherefore likewise the angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given ...
... base BC coincides with the base EF , the sides BA , AC cannot but coincide with the sides ED , DF ; wherefore likewise the angle BAC coincides with the angle EDF , and is equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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...