The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and ExercisesMacmillan, 1883 - 400 páginas |
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Página 7
... triangle on a given finite straight line . Let AB be the given straight line : it is required to describe an ... ABC shall be an equilateral triangle . Because the point A is the centre of the circle BCD , AC is equal to AB ...
... triangle on a given finite straight line . Let AB be the given straight line : it is required to describe an ... ABC shall be an equilateral triangle . Because the point A is the centre of the circle BCD , AC is equal to AB ...
Página 9
... ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , namely , AB to DE , and AC to DF , and the angle BAC equal to the angle ... triangle ABC be applied to the triangle BOOK I. 3 , 4 . 9.
... ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , namely , AB to DE , and AC to DF , and the angle BAC equal to the angle ... triangle ABC be applied to the triangle BOOK I. 3 , 4 . 9.
Página 10
... ABC be applied to the triangle DEF , so that the point A may be on the point D , and the straight line AB on the ... triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Axiom 8 . And the other angles of the one ...
... ABC be applied to the triangle DEF , so that the point A may be on the point D , and the straight line AB on the ... triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Axiom 8 . And the other angles of the one ...
Página 11
... ABC is equal to the remain- ing angle ACB , which are the angles at the base of the triangle ABC . [ Axiom 3 . And it has also been shewn that the angle FBC is equal to the angle GCB , which are the angles on the other side of the base ...
... ABC is equal to the remain- ing angle ACB , which are the angles at the base of the triangle ABC . [ Axiom 3 . And it has also been shewn that the angle FBC is equal to the angle GCB , which are the angles on the other side of the base ...
Página 12
... ABC be a triangle , having the angle ABC equal to the angle ACB : the side AC shall be equal to the side AB . one For if AC be not equal to AB , of them must be greater than the other . Let AB be the greater , and from it cut off DB ...
... ABC be a triangle , having the angle ABC equal to the angle ACB : the side AC shall be equal to the side AB . one For if AC be not equal to AB , of them must be greater than the other . Let AB be the greater , and from it cut off DB ...
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Términos y frases comunes
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
Pasajes populares
Página 262 - 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.
Página 71 - 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.
Página 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Página 182 - 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.
Página 8 - 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.
Página 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Página 58 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Página 60 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB
Página 242 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.
Página 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.