The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner CorrectedDesilver, 1829 - 516 páginas |
Dentro del libro
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Página 153
... greater segment , as the greater segment is to the less . IV . The altitude of any figure is the straight line drawn from its vertex perpendicular to the base . 1 * See Note . U PROP . I. THEOR . TRIANGLES and parallelograms of the THE ...
... greater segment , as the greater segment is to the less . IV . The altitude of any figure is the straight line drawn from its vertex perpendicular to the base . 1 * See Note . U PROP . I. THEOR . TRIANGLES and parallelograms of the THE ...
Página 154
... altitude are one to another as their bases . * Let the triangles ABC , ACD , and the parallelograms EC , CF , have the same altitude , viz . the perpendicular drawn from the point A to BD : then , as the base BC is to the base CD , so ...
... altitude are one to another as their bases . * Let the triangles ABC , ACD , and the parallelograms EC , CF , have the same altitude , viz . the perpendicular drawn from the point A to BD : then , as the base BC is to the base CD , so ...
Página 155
... altitudes , are one to another as their bases . Let the figures be placed so as to have their bases in the same ... altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for ...
... altitudes , are one to another as their bases . Let the figures be placed so as to have their bases in the same ... altitude , viz . the perpendicular drawn from the point E to AB , they are to one another as their bases ; and for ...
Página 227
... altitude , the insisting lines of which are terminated in the same straight lines in the plane opposite to the base , are equal to one another . * Let the solid parallelopipeds AH , AK be upon the same base AB , and of the same altitude ...
... altitude , the insisting lines of which are terminated in the same straight lines in the plane opposite to the base , are equal to one another . * Let the solid parallelopipeds AH , AK be upon the same base AB , and of the same altitude ...
Página 229
... altitude , the insisting straight lines of which are not terminated in the same straight lines in the plane opposite to the base , are equal to one another . * Let the parallelopipeds CM , CN be upon the same base AB , and of the same ...
... altitude , the insisting straight lines of which are not terminated in the same straight lines in the plane opposite to the base , are equal to one another . * Let the parallelopipeds CM , CN be upon the same base AB , and of the same ...
Otras ediciones - Ver todas
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Sin vista previa disponible - 2018 |
Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC multiple parallel parallelogram 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 AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 81 - The angles in the same segment of a circle are equal to one another.
Página 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Página 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Página 155 - 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 22 - ANY two angles of a triangle are together less than two right angles.
Página 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Página 24 - Any two sides of a triangle are together greater than the third side.