Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry |
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Page 24
... ABC , DEF be two triangles , which have the side AB equal to DE , and AC to DF ; and the angle A equal to D ; then the base BC will be equal to EF , and the triangle ABC to DEF ; and the other angles , to which the equal sides are op ...
... ABC , DEF be two triangles , which have the side AB equal to DE , and AC to DF ; and the angle A equal to D ; then the base BC will be equal to EF , and the triangle ABC to DEF ; and the other angles , to which the equal sides are op ...
Page 25
... ABC , DEF be two triangles which have the angles B , C equal to the angles E , F , each to each , and the side BC ... base of each triangle to be- come equal to each other , then the four angles at the bases of both triangles will be ...
... ABC , DEF be two triangles which have the angles B , C equal to the angles E , F , each to each , and the side BC ... base of each triangle to be- come equal to each other , then the four angles at the bases of both triangles will be ...
Page 26
... ABC be a triangle , of which the side AB is equal to AC ; the angle ABC is ... base FC is equal to GB ( 4. 1. ) , and the angle ACF to ABG , and the angle ... ABC is equal to the remaining angle ACB ( 3 Ax . ) . There- fore , the angles ...
... ABC be a triangle , of which the side AB is equal to AC ; the angle ABC is ... base FC is equal to GB ( 4. 1. ) , and the angle ACF to ABG , and the angle ... ABC is equal to the remaining angle ACB ( 3 Ax . ) . There- fore , the angles ...
Page 27
... base of each triangle are equal to each other . Q. E. D. ED . Cor . Hence every equilateral triangle is also equiangular , Let ABC be an equilateral triangle ; then because the two sides AB , AC are equal , the angles B and C at the base ...
... base of each triangle are equal to each other . Q. E. D. ED . Cor . Hence every equilateral triangle is also equiangular , Let ABC be an equilateral triangle ; then because the two sides AB , AC are equal , the angles B and C at the base ...
Page 35
... ABC be a triangle and let one side BC be produced to D ; the exterior angle ACD is greater than either of the inte ... base AB is equal to the base CF ( 4. 1. ) , and the angle BAE is equal to B the angle ECF . But the angle ECD is ...
... ABC be a triangle and let one side BC be produced to D ; the exterior angle ACD is greater than either of the inte ... base AB is equal to the base CF ( 4. 1. ) , and the angle BAE is equal to B the angle ECF . But the angle ECD is ...
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Elements of Geometry: Being Chiefly a Selection From Playfair's Geometry John Playfair No preview available - 2023 |
Elements of Geometry: Being Chiefly a Selection From Playfair's Geometry John Playfair No preview available - 2023 |
Common terms and phrases
ABC is equal ABCD alternate angles angle ABC angle ACB angle BAC angles AGH angles equal base ABC bases and altitudes bisect centre chord circumference cone Consequently cylinder demonstrations described diagonals diameter divided draw equal angles equal arches equal bases equal circles equal to AC equiangular Euclid's Euclid's Elements exterior angle fore four quantities four right angles geometry given point given straight line gles greater Hence homologous sides intersect KLMN Let ABC meet opposite angles opposite side paral parallel lines parallel to CD parallelogram parallelopipeds perp perpendicular plane polygon prism Prop pyramid Q. E. D. COR Q. E. D. PROPOSITION radius rectangle contained right angled triangle Scholium segments semicircle side AC similar similar triangles solid square straight line &c subtended tangent THEOREM triangle ABC vertex wherefore
Popular passages
Page 36 - Any two sides of a triangle are together greater than the third side.
Page 80 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 42 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line...
Page 30 - To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line : it is required to divide it intotwo equal parts.
Page 20 - LET it be granted that a straight line may be drawn from any one point to any other point.
Page 38 - Problem. At a given point in a given straight line to make a rectilineal angle equal to a given rectilineal angle.
Page 113 - Wherefore also the angle BAD is equal to the angle CAD : Therefore the angle BAC is cut into two equal angles by the straight line AD.
Page 24 - DE ; the point B shall coincide with the point E, because AB is equal to DE; and AB coinciding with DE, AC shall coincide...
Page 36 - The greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.