The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and TwelfthBell & Bradfute, 1835 - 513 páginas |
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Página 13
... base AD is equal to the base DB , and the straight line AB is divided into two equal parts in the point D. Which was to be done . C Book I. c 4. 1 . A D B PROP . XI . PROB . To draw a straight line at right angles to a given straight ...
... base AD is equal to the base DB , and the straight line AB is divided into two equal parts in the point D. Which was to be done . C Book I. c 4. 1 . A D B PROP . XI . PROB . To draw a straight line at right angles to a given straight ...
Página 14
... base CF is equal to the base CG ; therefore the angle CHF is equal to the angle CHG ; and they are adjacent angles ; but when a straight line standing on a straight line makes the adjacent angles equal to one another , each of them is a ...
... base CF is equal to the base CG ; therefore the angle CHF is equal to the angle CHG ; and they are adjacent angles ; but when a straight line standing on a straight line makes the adjacent angles equal to one another , each of them is a ...
Página 17
... base AB is equal to the base CF , and c 4. 1 . the triangle AEB to the triangle CEF , and the remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the ...
... base AB is equal to the base CF , and c 4. 1 . the triangle AEB to the triangle CEF , and the remaining angles to the remaining angles , each to each , to which the equal sides are opposite ; wherefore the angle BAE is equal to the ...
Página 21
... base DE to the base FG ; the angle DCE is equal to the angle FAG . Therefore at b 8. 1 . the given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . Which was to be done . PROP ...
... base DE to the base FG ; the angle DCE is equal to the angle FAG . Therefore at b 8. 1 . the given point A in the given straight line AB , the angle FAG is made equal to the given rectilineal angle DCE . Which was to be done . PROP ...
Página 22
... base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other , and at the point D ... base BC is equal to the base EG ; and be- cause DG is equal to DF , the angle DFG is equal to d D the angle DGF ; but ...
... base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other , and at the point D ... base BC is equal to the base EG ; and be- cause DG is equal to DF , the angle DFG is equal to d D the angle DGF ; but ...
Otras ediciones - Ver todas
The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson Sin vista previa disponible - 2019 |
Términos y frases comunes
ABC is given altitude angle ABC angle BAC arch base BC BC is equal bisected Book XI centre circle ABCD circumference cone cosine 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 gles gnomon greater half the perimeter hypotenuse join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelepiped spherical angle square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC vertex wherefore
Pasajes populares
Página 47 - If a straight line be bisected and produced to any point, the rectangle contained by the whole line thus produced and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. Let the straight line AB be bisected in C, and produced to D : the rectangle AD, DB, together with the square of CB, shall be equal to the square of CD.
Página 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Página 26 - if a straight line," &c. QED PROP. XXIX. THEOR. See the Jf a straight line fall upon two parallel straight ti?isepropo- lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.
Página 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Página 170 - 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 of the ratios of their sides. • See Note. Let BG, CG, be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Página 153 - 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 30 - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
Página 28 - 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 64 - ... than the more remote: but of those which fall upon the convex circumference, the least is that between the point without the circle and the diameter; and, of the rest, that which is nearer to the least is always less than the more remote: and only two equal straight lines can be drawn from the point into the circumference, one upon each side of the least.
Página 5 - 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...