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 σελίδες |
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Σελίδα 9
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which B CE the equal sides are opposite , shall be equal , each to each , viz . the angle ABC ...
... angle BAC equal to the angle EDF , the base BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles to which B CE the equal sides are opposite , shall be equal , each to each , viz . the angle ABC ...
Σελίδα 12
... angle ACD is equal † to the angle ADC : but the angle ACD is greater than the angle BCD ; there- fore the angle ADC ... BAC is equal to the angle EDF . G For , if the triangle ABC be applied to DEF 12 EUCLID'S ELEMENTS .
... angle ACD is equal † to the angle ADC : but the angle ACD is greater than the angle BCD ; there- fore the angle ADC ... BAC is equal to the angle EDF . G For , if the triangle ABC be applied to DEF 12 EUCLID'S ELEMENTS .
Σελίδα 13
... angle BAC coincides with the angle EDF , and is equal to it . Therefore if two triangles , 1 8 Ax . & c . Q. E. D. PROPOSITION IX . PROB . — To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be ...
... angle BAC coincides with the angle EDF , and is equal to it . Therefore if two triangles , 1 8 Ax . & c . Q. E. D. PROPOSITION IX . PROB . — To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be ...
Σελίδα 17
... angles ; but the angles ABC , ABD are likewise together equal to two right angles ; + Hyp . therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the re- maining angle ... BAC . 3 Ax . * 10. 1 . + ...
... angles ; but the angles ABC , ABD are likewise together equal to two right angles ; + Hyp . therefore the angles CBA , ABE are equal to the angles CBA , ABD : take away the common angle ABC , the re- maining angle ... BAC . 3 Ax . * 10. 1 . + ...
Σελίδα 18
... angle AEB , is equal to the angle CEF , because they are opposite vertical angles ; therefore B the base AB is equal ... BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROPOSITION ...
... angle AEB , is equal to the angle CEF , because they are opposite vertical angles ; therefore B the base AB is equal ... BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROPOSITION ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 12 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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
Σελίδα 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.
Σελίδα 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.
Σελίδα 66 - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Σελίδα 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.