The First Six Books: Together with the Eleventh and TwelfthJ. Balfour, 1781 - 520 pages |
From inside the book
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Page 6
... thefe Elements . In like manner , in the Demonftration of the 26th Prop . of the 11th Book , it is taken for granted , that thofe folid Angles are e- qual to one another which are contained by plain Angles of the fame Number and ...
... thefe Elements . In like manner , in the Demonftration of the 26th Prop . of the 11th Book , it is taken for granted , that thofe folid Angles are e- qual to one another which are contained by plain Angles of the fame Number and ...
Page 7
... thefe Elements are the Foundation of a Science by which the Investigation and Discovery of ufeful Truths , at leaft in Mathematical Learn- ing , is promoted as far as the limited Powers of the Mind al- low ; and which likewife is of the ...
... thefe Elements are the Foundation of a Science by which the Investigation and Discovery of ufeful Truths , at leaft in Mathematical Learn- ing , is promoted as far as the limited Powers of the Mind al- low ; and which likewife is of the ...
Page 12
... oppofite fides equal to ond another , but all its fides are not equal , nor its angles right angles . XXXIV . All other four fided figures befides thefe , XXXXIV 32 THE ELEMENTS An acute angled triangle, is that which has three ...
... oppofite fides equal to ond another , but all its fides are not equal , nor its angles right angles . XXXIV . All other four fided figures befides thefe , XXXXIV 32 THE ELEMENTS An acute angled triangle, is that which has three ...
Page 13
... thefe , are called Trapeziums . XXXV . Parallel ftraight lines , are fuch as are in the fame plane , and which , being produced ever fo far both ways , do not meet . Book I. LE POSTULATES . I. ET it be granted that a straight line may ...
... thefe , are called Trapeziums . XXXV . Parallel ftraight lines , are fuch as are in the fame plane , and which , being produced ever fo far both ways , do not meet . Book I. LE POSTULATES . I. ET it be granted that a straight line may ...
Page 24
... thefe equals ; there- fore the angles CBE , EBD are equal to the three angles CBA , ABE , EBD . Again , because the angle DBA is equal to the two angles DBE , EBA , add to thefe equals the angle ABC ; therefore the angles DBA , ABC are ...
... thefe equals ; there- fore the angles CBE , EBD are equal to the three angles CBA , ABE , EBD . Again , because the angle DBA is equal to the two angles DBE , EBA , add to thefe equals the angle ABC ; therefore the angles DBA , ABC are ...
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Common terms and phrases
alfo alſo angle ABC angle BAC bafe baſe BC is equal BC is given becauſe the angle becauſe the ratio bifected Book XI cafe centre circle ABCD circumference cone confequently cylinder defcribed demonftrated drawn EFGH equal angles equiangular equimultiples Euclid excefs faid fame manner fame multiple fame ratio fame reafon fecond fegment fide BC fides fimilar firft firſt folid angle fome fore fphere fquare of AC ftraight line AB ftraight line BC given angle given ftraight line given in fpecies given in magnitude given in pofition given magnitude given ratio gnomon greater join lefs likewife oppofite parallel parallelepipeds parallelogram perpendicular plane angles prifms PROP propofition pyramid ratio of BC rectangle contained rectilineal figure right angles ſquare thefe THEOR theſe triangle ABC wherefore
Popular passages
Page 472 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Page 170 - 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 81 - THE straight line drawn at right angles to the diameter of a circle, from the extremity of...
Page 105 - DEF are likewise equal (13. i.) to two right angles ; therefore the angles AKB, AMB are equal to the angles DEG, DEF, of which AKB is equal to DEG ; wherefore the remaining angle AMB is equal to the remaining angle DEF.
Page 167 - AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off.
Page 10 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle; and the straight line which stands on the other is called a perpendicular to it.
Page 62 - AB be the given straight line ; it is required to divide it 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 112 - To describe an equilateral and equiangular pentagon about a given circle. • Let ABCDE be the given circle; it is required to describe an equilateral and equiangular pentagon about the circle ABCDE. Let the angles of a pentagon, inscribed in the circle...
Page 200 - 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 38 - F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.