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 |
From inside the book
Results 1-5 of 100
Page 14
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post . ) the ...
... greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post . ) the ...
Page 17
... greater , and from it cut ( 3. 1. ) off DB- equal to AC , the less , and join DC ; therefore , because in the ... greater also than BCD ; much more then is the angle BDC greater than A B the angle BCD . Again , because CB is equal ...
... greater , and from it cut ( 3. 1. ) off DB- equal to AC , the less , and join DC ; therefore , because in the ... greater also than BCD ; much more then is the angle BDC greater than A B the angle BCD . Again , because CB is equal ...
Page 18
... greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BDC ; but BCD has been proved to be greater than the same BCD ; which ...
... greater than BCD ; much more then is the angle BDC greater than the angle BCD . Again , because CB is equal to DB , the angle BDC is equal ( 5. 1. ) to the angle BDC ; but BCD has been proved to be greater than the same BCD ; which ...
Page 24
... greater than the angle ECF ; therefore the angle ACD is greater than BAE : in the same manner , if the side BC be bisected , it may be demonstrat- ed that the angle BCG , that is , ( 15. 1. ) the angle ACD , is great- er than the angle ...
... greater than the angle ECF ; therefore the angle ACD is greater than BAE : in the same manner , if the side BC be bisected , it may be demonstrat- ed that the angle BCG , that is , ( 15. 1. ) the angle ACD , is great- er than the angle ...
Page 25
... greater than the angles ABC , ACB ; but ACD , ACB are together equal ( 13. 1. ) to two right angles ; therefore the ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC ...
... greater than the angles ABC , ACB ; but ACD , ACB are together equal ( 13. 1. ) to two right angles ; therefore the ... greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC ...
Other editions - View all
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.