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 11
... which are the angles on the other side of the base . Wherefore , the angles & c . Q.E.D. Corollary . Hence every equilateral triangle is also equiangular . PROPOSITION 6. THEOREM . If two angles of a triangle BOOK I. 5 . 11.
... which are the angles on the other side of the base . Wherefore , the angles & c . Q.E.D. Corollary . Hence every equilateral triangle is also equiangular . PROPOSITION 6. THEOREM . If two angles of a triangle BOOK I. 5 . 11.
Página 12
... Corollary . Hence every equiangular triangle is also equilateral . PROPOSITION 7. THEOREM . On the same base , and on the same side of it , there can- not be two triangles having their sides which are terminated at one extremity of the ...
... Corollary . Hence every equiangular triangle is also equilateral . PROPOSITION 7. THEOREM . On the same base , and on the same side of it , there can- not be two triangles having their sides which are terminated at one extremity of the ...
Página 16
... Corollary . By the help of this problem it may be shewn that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB com- mon to both of them . From the point B draw ...
... Corollary . By the help of this problem it may be shewn that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB com- mon to both of them . From the point B draw ...
Página 20
... Corollary 1. From this it is manifest that , if two straight lines cut one another , the angles which they make at the point where they cut , are together equal to four right angles . Corollary 2. And consequently , that all the angles ...
... Corollary 1. From this it is manifest that , if two straight lines cut one another , the angles which they make at the point where they cut , are together equal to four right angles . Corollary 2. And consequently , that all the angles ...
Página 35
... ; therefore also the angles CBA , BAC , ACB are together equal to two right angles . Wherefore , if a side of any triangle & c . [ I. 13 , [ Axiom 1 . Q.E.D. COROLLARY 1. All the interior angles of any recti- lineal 3-2 BOOK I. 31 , 32 .
... ; therefore also the angles CBA , BAC , ACB are together equal to two right angles . Wherefore , if a side of any triangle & c . [ I. 13 , [ Axiom 1 . Q.E.D. COROLLARY 1. All the interior angles of any recti- lineal 3-2 BOOK I. 31 , 32 .
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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.