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 24
... reason , the exterior angle CEB of the tri- angle ABE is greater than the angle BAE . But it has been shewn that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle ВАС . Wherefore , if ...
... reason , the exterior angle CEB of the tri- angle ABE is greater than the angle BAE . But it has been shewn that the angle BDC is greater than the angle CEB ; much more then is the angle BDC greater than the angle ВАС . Wherefore , if ...
Page 39
... reason EF is equal to BC ; therefore AD is equal to EF ; B [ I. 34 . [ Axiom 1 . therefore the whole , or the remainder , AE is equal to the whole , or the remainder , DF . And AB is equal to DC ; [ Axioms 2 , 3 . [ I. 34 . therefore ...
... reason EF is equal to BC ; therefore AD is equal to EF ; B [ I. 34 . [ Axiom 1 . therefore the whole , or the remainder , AE is equal to the whole , or the remainder , DF . And AB is equal to DC ; [ Axioms 2 , 3 . [ I. 34 . therefore ...
Page 40
... reason the parallelogram EFGH is equal to the same EBCH . Therefore the parallelogram ABCD is equal to the par- allelogram EFĜH . Wherefore , parallelograms & c . Q.E.D. PROPOSITION 37. THEOREM . [ Axiom 1 . Triangles on the same base ...
... reason the parallelogram EFGH is equal to the same EBCH . Therefore the parallelogram ABCD is equal to the par- allelogram EFĜH . Wherefore , parallelograms & c . Q.E.D. PROPOSITION 37. THEOREM . [ Axiom 1 . Triangles on the same base ...
Page 45
... reason the triangle KGC is equal to the triangle KFC . Therefore , because the triangle AEK is equal to the tri- angle AHK , and the triangle KGC to the triangle KFC ; the triangle AEK together with the triangle KGC is equal to the ...
... reason the triangle KGC is equal to the triangle KFC . Therefore , because the triangle AEK is equal to the tri- angle AHK , and the triangle KGC to the triangle KFC ; the triangle AEK together with the triangle KGC is equal to the ...
Page 50
... reason , AB and AH are in the same straight line . Now the angle DBC is equal to the angle FBA , for each of them is a right angle . Add to each the angle ABC . [ Axiom 11 . [ Axiom 2 . Therefore the whole angle DBA is equal to the ...
... reason , AB and AH are in the same straight line . Now the angle DBC is equal to the angle FBA , for each of them is a right angle . Add to each the angle ABC . [ Axiom 11 . [ Axiom 2 . Therefore the whole angle DBA is equal to the ...
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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.