The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh and Twelfth ; the Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored ; Also the Book of Euclid's Data, in Like Manner Corrected |
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Page 15
... THEOR . 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 . Let ABC be an isosceles triangle , of which the side ...
... THEOR . 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 . Let ABC be an isosceles triangle , of which the side ...
Page 16
... THEOR . If two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal an- gles , shall be equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ...
... THEOR . If two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal an- gles , shall be equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ...
Page 17
... THEOR . 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 one an- other , and likewise those which are terminated in the ...
... THEOR . 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 one an- other , and likewise those which are terminated in the ...
Page 18
... THEOR . 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 ; the angle which is contained by the two sides of the one shall be equal to the angle contained by ...
... THEOR . 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 ; the angle which is contained by the two sides of the one shall be equal to the angle contained by ...
Page 23
... THEOR . IF two straight lines cut one another , the vertical or opposite angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB , and CEB to AED ...
... THEOR . IF two straight lines cut one another , the vertical or opposite angles shall be equal . Let the two straight lines AB , CD cut one another in the point E ; the angle AEC shall be equal to the angle DEB , and CEB to AED ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |
Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference co-sine cone 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 gnomon greater join less Let ABC multiple opposite parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Popular passages
Page 9 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 81 - The angles in the same segment of a circle are equal to one another.
Page 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Page 33 - 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 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Page 96 - 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.
Page 155 - 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.
Page 22 - ANY two angles of a triangle are together less than two right angles.
Page 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.
Page 24 - Any two sides of a triangle are together greater than the third side.