Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books and the First Twenty-one Propositions of the Eleventh Book ...T. Stevenson, 1845 - 199 páginas |
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Página 35
... passes ; and BK , KD the other parallel- ograms which make up the whole figure ABCD , which are therefore called the complements . The complement BK is equal to the complement KD . * 34. 1 . + 2 Ax . 3 Ax BOOK I. PROP . XLII . XLIII . 35.
... passes ; and BK , KD the other parallel- ograms which make up the whole figure ABCD , which are therefore called the complements . The complement BK is equal to the complement KD . * 34. 1 . + 2 Ax . 3 Ax BOOK I. PROP . XLII . XLIII . 35.
Página 58
... pass through the centre , it shall cut it at right angles : and if it cut it at right angles , it shall besect it . Let ABC be a circle ; and let CD , a straight line drawn through the centre , bisect any straight line AB , which does ...
... pass through the centre , it shall cut it at right angles : and if it cut it at right angles , it shall besect it . Let ABC be a circle ; and let CD , a straight line drawn through the centre , bisect any straight line AB , which does ...
Página 59
... pass through the centre : AC , BD do not bisect one another . For , if it is possible , let AE be equal to EC , and BE to ED : if one of the lines pass through the centre , it is plain that it cannot be bisected by the other which does ...
... pass through the centre : AC , BD do not bisect one another . For , if it is possible , let AE be equal to EC , and BE to ED : if one of the lines pass through the centre , it is plain that it cannot be bisected by the other which does ...
Página 60
... passes through the centre , is always greater than one more remote : and from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . Let ABCD be a circle , and ...
... passes through the centre , is always greater than one more remote : and from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . Let ABCD be a circle , and ...
Página 61
... passes through the centre , is equal to one which is more remote ; which is impossible . Therefore , if any point be taken , & c . Q. E. D. PROPOSITION VIII . THEOR . - If any point be taken without a circle , and straight lines be ...
... passes through the centre , is equal to one which is more remote ; which is impossible . Therefore , if any point be taken , & c . Q. E. D. PROPOSITION VIII . THEOR . - If any point be taken without a circle , and straight lines be ...
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Términos y frases comunes
ABCD adjacent angles angle ABC angle ACB angle BAC angle BCD angle DEF angle EDF angles equal base BC BC is equal bisected centre circle ABC Constr describe diameter double draw equal angles equal to F equiangular equimultiples ex æquali exterior angle fore four magnitudes fourth given circle given straight line gnomon greater ratio join less Let ABC Let the straight likewise meet multiple opposite angle parallel to BC parallelogram perpendicular plane polygon proportionals Q. E. D. PROPOSITION rectangle contained remaining angle right angles segment semicircle sides square of AC straight line AB straight line AC THEOR THEOR.-If three straight lines tiple touches the circle triangle ABC triangle DEF twice the rectangle wherefore
Pasajes populares
Página 12 - If two triangles have two sides of the one equal to two sides of the...
Página 29 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Página 143 - 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 69 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle ; the angles which this line makes with the line touching the circle, shall be equal to the angles which are in the alternate segments of the circle.
Página 20 - If from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let the two straight lines BD.
Página 102 - A LESS magnitude is said to be a part of a greater magnitude, when the less measures the greater; that is, ' when the less is contained a certain number of times
Página 44 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Página 71 - The opposite angles of any quadrilateral figure described in a circle, are toe/ether equal to two right angles. Let ABCD be a quadrilateral figure in the circle ABCD : any two of its opposite angles are together equal to two right angles.
Página 66 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Página 83 - 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.