The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and TwelfthBell & Bradfute, 1835 - 513 ページ |
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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
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47 ページ - 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.
306 ページ - 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.
26 ページ - 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.
54 ページ - 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...
170 ページ - 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.
153 ページ - 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.
30 ページ - And because the angle ABC is equal to the angle BCD, and the angle CBD to the angle ACB...
28 ページ - 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.
64 ページ - ... 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.
5 ページ - 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...