The school Euclid: comprising the first four books, by A.K. Isbister1863 |
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Página 6
... triangle upon a given finite straight line . * ( References - Def . 15 ; ax . 1 ; post . 1 , 3. ) Let AB be the ... ABC shall be an equilateral triangle . DEMONSTRATION Because the point A is the centre of the circle BCD , therefore AC ...
... triangle upon a given finite straight line . * ( References - Def . 15 ; ax . 1 ; post . 1 , 3. ) Let AB be the ... ABC shall be an equilateral triangle . DEMONSTRATION Because the point A is the centre of the circle BCD , therefore AC ...
Página 9
... triangle ABC to the triangle DEF , and the other angles to which the equal sides are oppo- site , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . D Δ . Δ . E DEMONSTRATION For , if the ...
... triangle ABC to the triangle DEF , and the other angles to which the equal sides are oppo- site , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . D Δ . Δ . E DEMONSTRATION For , if the ...
Página 10
... triangle are equal to another ; one and if the equal sides be produced , the angles upon the other side of the base shall be equal . ( References - Prop . I. 3 , 4 ; ax . 3. ) Let ABC be an isosceles triangle , of which the side AB is ...
... triangle are equal to another ; one and if the equal sides be produced , the angles upon the other side of the base shall be equal . ( References - Prop . I. 3 , 4 ; ax . 3. ) Let ABC be an isosceles triangle , of which the side AB is ...
Página 11
... ABC is equal to the remaining angle ACB , which are the angles at the base of the triangle ABC . And it has been proved , that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore ...
... ABC is equal to the remaining angle ACB , which are the angles at the base of the triangle ABC . And it has been proved , that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . Therefore ...
Página 12
Euclides Alexander Kennedy Isbister. Let the triangle ABC have the angle ABC equal to the angle ACB . Then the side AB shall be equal to the side AC . B CONSTRUCTION For , if AB be not equal to AC , one of them is greater than the other ...
Euclides Alexander Kennedy Isbister. Let the triangle ABC have the angle ABC equal to the angle ACB . Then the side AB shall be equal to the side AC . B CONSTRUCTION For , if AB be not equal to AC , one of them is greater than the other ...
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The School Euclid: Comprising the First Four Books, Chiefly from the Text of ... A. K. Isbister Sin vista previa disponible - 2009 |
Términos y frases comunes
adjacent angles alternate angles angle ABC angle BAC angle BCD angle EDF angle equal base BC BC is equal bisect centre circle ABC constr CONSTRUCTION cuts the circle DEMONSTRATION describe a circle describe the circle diameter double equal angles equal straight lines equal to BC equiangular pentagon equilateral and equiangular equilateral triangle Euclid exterior angle Geography given circle given point given rectilineal angle given straight line given triangle gnomon greater inscribed interior and opposite isosceles triangle less Let ABC Let the straight Ludgate Hill opposite angles parallel parallelogram pentagon perpendicular post 8vo produced Q. E. D. PROP rectangle contained rectilineal figure References Prop References-Prop remaining angle right angles segment semicircle side BC square of AC straight line AC THEOREM touches the circle triangle ABC twice the rectangle
Pasajes populares
Página 94 - A CONSTRUCTION For, if not let it fall otherwise, if possible, as FGDB; let F be the centre of the circle ABC, and G the centre of ADE. Join AF and AG. DEMONSTRATION Because two sides of a triangle are together greater than the third side therefore AG, GF, are greater than FA;
Página 17 - and they are adjacent angles. But, ' 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;' (def. 10) therefore each of the angles DCF, ECF, is a right angle. Wherefore, from the point C, in the straight line AB,
Página xvii - to the same two, and when the adjacent angles are equal, they are right angles. Prop. 32. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle; the angles made by this line with the line touching the circle, shall be
Página ii - at right angles to a given straight line, from a given point in the same. Prop. 13. The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Prop. 14. If, at a point in a straight line, two other straight lines,
Página 2 - XV. A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another. XVL And this point is called the centre of the circle.
Página ix - line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Página 118 - (i. 32) and when the adjacent angles are equal, they are right angles, (i. def. 10.) PROP. XXXII. —THEOREM. If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle; then the angles made by this line with the line
Página iii - to four right angles. Prop. 16. If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. Prop. 17. Any two angles of a triangle are together less than two right angles. Prop.
Página 47 - Wherefore, triangles, &c. QED PROP. XXXVIII THEOREM. Triangles upon equal bases and between the same parallels are equal to one another. (References — Prop. i. 31, 34, 36 ; ax. 7.) Let the triangles ABC, DEF, be on the equal bases BC, EF, and between the same parallels AD, BF. Then
Página 23 - two angles of a triangle are together less than two right angles. Then any two of its angles shall be together less than two right angles, A CONSTRUCTION Produce the side BC to D. DEMONSTRATION Because ACD is the exterior angle of the triangle ABC, therefore the angle ACD is greater than the interior and opposite angle