The Elements of Euclid for the Use of Schools and Colleges: With Notes, an Appendix, and Exercises. comprising the first six books and portions of the eleventh and twelfth books |
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Page 10
... fall on DF , because the angle BAC is equal to the angle EDF . [ Hyp . B [ Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with ...
... fall on DF , because the angle BAC is equal to the angle EDF . [ Hyp . B [ Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with ...
Page 30
... . therefore the base AC is equal to the base DF , and the third angle BAC to the third angle EDF . Wherefore , if two triangles & c . Q.E.D. [ I. 4 . PROPOSITION 27 . THEOREM . If a straight line falling 30 EUCLID'S ELEMENTS .
... . therefore the base AC is equal to the base DF , and the third angle BAC to the third angle EDF . Wherefore , if two triangles & c . Q.E.D. [ I. 4 . PROPOSITION 27 . THEOREM . If a straight line falling 30 EUCLID'S ELEMENTS .
Page 31
... falling on two other straight lines , make the alternate angles equal to one another , the two straight lines shall be parallel to one another . Let the straight line EF , which falls on the two straight lines AB , CD , make the ...
... falling on two other straight lines , make the alternate angles equal to one another , the two straight lines shall be parallel to one another . Let the straight line EF , which falls on the two straight lines AB , CD , make the ...
Page 32
... fall on two parallel straight lines , it makes the alternate angles equal to one another , and the exterior angle equal to the interior and opposite angle on the same side ; and also the two interior angles on the same side together ...
... fall on two parallel straight lines , it makes the alternate angles equal to one another , and the exterior angle equal to the interior and opposite angle on the same side ; and also the two interior angles on the same side together ...
Page 35
... falls on them , the alternate angles x BAC , ACE are equal . D [ I. 29 . Again , because AB is parallel to CE , and BD falls on them , the exterior angle EOD is equal to the interior and opposite angle ABC . [ I. 29 . But the angle ACE ...
... falls on them , the alternate angles x BAC , ACE are equal . D [ I. 29 . Again , because AB is parallel to CE , and BD falls on them , the exterior angle EOD is equal to the interior and opposite angle ABC . [ I. 29 . But the angle ACE ...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ... Issac Todhunter No preview available - 2014 |
Common terms and phrases
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore
Popular passages
Page 225 - 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.
Page 284 - 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 73 - 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 39 - Triangles upon the same base, and between the same parallels, are equal to one another.
Page 10 - 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 353 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Page 67 - ... subtending the obtuse angle, is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle, Let ABC be an obtuse-angled triangle, having the obtuse angle ACB; and from the point A, let AD be drawn perpendicular to BC produced.
Page 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Page xv - PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given Jinite straight line. Let AB be the given straight line. It is required to describe an equilateral triangle upon AB, From the centre A, at the distance AB, describe the circle BCD ; (post.
Page 36 - 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.