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 104
... Ratio is a mutual relation of two magnitudes of the same ' kind to one another , in respect of quantity . ' IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The ...
... Ratio is a mutual relation of two magnitudes of the same ' kind to one another , in respect of quantity . ' IV . Magnitudes are said to have a ratio to one another , when the less can be multiplied so as to exceed the other . V. The ...
Página 105
... ratio than the third magnitude has to the fourth : and , on the contrary , the third is said to have to the fourth a less ratio than the first has to the second . VIII . ' Analogy , or proportion , is the similitude of ratios . ' IX ...
... ratio than the third magnitude has to the fourth : and , on the contrary , the third is said to have to the fourth a less ratio than the first has to the second . VIII . ' Analogy , or proportion , is the similitude of ratios . ' IX ...
Página 105
... ratio of B to C , and the ratio of C to D ; or , the ratio of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has to F ; and B to C the same ratio that G has to H ...
... ratio of B to C , and the ratio of C to D ; or , the ratio of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has to F ; and B to C the same ratio that G has to H ...
Página 106
... ratio of B to C , and the ratio of C to D ; or , the ratio of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has to F ; and B to C the same ratio that G has to H ...
... ratio of B to C , and the ratio of C to D ; or , the ratio of A to D is said to be compounded of the ratios of A to B , B to C , and C to D. And if A has to B the same ratio which E has to F ; and B to C the same ratio that G has to H ...
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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.