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 |
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Página 10
... square is that which has all its sides equal , and all its angles right angles . XXXI . An oblong , is that which has all its angles right angles , but has not all its sides equal . XXXII . A rhombus , is that which has all its sides ...
... square is that which has all its sides equal , and all its angles right angles . XXXI . An oblong , is that which has all its angles right angles , but has not all its sides equal . XXXII . A rhombus , is that which has all its sides ...
Página 45
... , viz . by applying ( 44. 1. ) to the given straight line a parallelogram equal to the first triangle ABD , and having an angle equal to the given angle . PROP . XLVI . PROB . To describe a square BOOK I. 45 THE ELEMENTS OF EUCLID .
... , viz . by applying ( 44. 1. ) to the given straight line a parallelogram equal to the first triangle ABD , and having an angle equal to the given angle . PROP . XLVI . PROB . To describe a square BOOK I. 45 THE ELEMENTS OF EUCLID .
Página 46
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . From the point A draw ( 11. 1. ) AC at right angles to AB ; and make ( 3. 1. ) AD equal to AB , and through the point ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . From the point A draw ( 11. 1. ) AC at right angles to AB ; and make ( 3. 1. ) AD equal to AB , and through the point ...
Página 47
... square GB and in the same manner , by joining AE , BK , it is demonstrated that the paralle- logram CL is equal to the square HC : therefore the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is described ...
... square GB and in the same manner , by joining AE , BK , it is demonstrated that the paralle- logram CL is equal to the square HC : therefore the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is described ...
Página 48
... square described upon BC , one of the sides of the tri- angle ABC , be equal to the squares upon the other sides BA ... square of DA is equal to the square of AB : to each of these add the square of AC : therefore the squares of DA , AC ...
... square described upon BC , one of the sides of the tri- angle ABC , be equal to the squares upon the other sides BA ... square of DA is equal to the square of AB : to each of these add the square of AC : therefore the squares of DA , AC ...
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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.