The College Euclid: Comprising the First Six and the Parts of the Eleventh and Twelfth Books Read at the Universities ... By A. K. Isbister1865 |
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Page 10
Euclides Alexander Kennedy ISBISTER. PROP . V. - THEOREM . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal ...
Euclides Alexander Kennedy ISBISTER. PROP . V. - THEOREM . The angles at the base of an isosceles triangle are equal to one another ; and if the equal sides be produced , the angles upon the other side of the base shall be equal ...
Page 12
... THEOREM . Upon the same base and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to each other , and likewise those which are terminated in the other ...
... THEOREM . Upon the same base and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to each other , and likewise those which are terminated in the other ...
Page 14
... THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; then the angle which is contained by the two sides of the one shall be equal to the angle ...
... THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal ; then the angle which is contained by the two sides of the one shall be equal to the angle ...
Page 19
... THEOREM . The angles which one straight line makes with another upon one side of it , are either two right angles , or are together equal to two right angles . ( References - Prop . I. 11 ; ax . 1 , 2 ; def . 10. ) Let the straight line ...
... THEOREM . The angles which one straight line makes with another upon one side of it , are either two right angles , or are together equal to two right angles . ( References - Prop . I. 11 ; ax . 1 , 2 ; def . 10. ) Let the straight line ...
Page 21
Euclides Alexander Kennedy ISBISTER. PROP . XIV . - THEOREM . If , at a point in a straight line , two other straight lines , upon the oppo- site sides of it , make the adjacent angles ... THEOREM . If two straight BOOK I. PROP . XIV . 17 21.
Euclides Alexander Kennedy ISBISTER. PROP . XIV . - THEOREM . If , at a point in a straight line , two other straight lines , upon the oppo- site sides of it , make the adjacent angles ... THEOREM . If two straight BOOK I. PROP . XIV . 17 21.
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Common terms and phrases
ABCD AC is equal adjacent angles angle ABC angle ACB angle BAC angle equal base BC bisect Book centre circle ABC circumference compounded constr DEMONSTRATION diameter double draw Edition English equal angles equal straight lines equal to BC equiangular equilateral and equiangular equimultiples Euclid exterior angle four magnitudes fourth French given circle given point given rectilineal angle given straight line gnomon Grammar greater ratio inscribed isosceles triangle join less Let ABC multiple opposite angles parallel parallelogram pentagon perpendicular plane polygon proportionals proposition Q. E. D. PROP rectangle contained rectilineal figure References-Prop remaining angle right angles segment similar solid angle square of AC straight line AC THEOREM third three straight lines touches the circle triangle ABC twice the rectangle wherefore
Popular passages
Page 140 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Page xiv - The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle...
Page 310 - IF a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles ; and the three interior angles of every triangle are equal to two right angles.
Page 33 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page vi - If a straight line be divided into any two parts, four times the rectangle contained ~by the whole line and one of the parts, together with the square on the other part, is equal to the square on the straight line which is made up of the whole and that part.
Page 310 - 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.
Page xxxvii - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Page 69 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square of the other part.
Page 287 - If any point be taken in the diameter of a circle which is not the centre, of all the straight lines which can be drawn from it to the circumference, the greatest is that in which the centre is, and the other part of that diameter is the least...