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 Seiten |
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Seite 8
... Axiom 3 . But it has been shewn that BC is equal to BG ; therefore AL and BC are each of them equal to BG . But things which are equal to the same thing are equal to one another . [ Axiom 1 . Therefore AL is equal to BC . Wherefore from ...
... Axiom 3 . But it has been shewn that BC is equal to BG ; therefore AL and BC are each of them equal to BG . But things which are equal to the same thing are equal to one another . [ Axiom 1 . Therefore AL is equal to BC . Wherefore from ...
Seite 10
... Axiom 10 . Therefore the base BC coincides with the base EF , and is equal to it . [ Axiom 8 . Therefore the whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Axiom 8 . And the other angles of the one ...
... Axiom 10 . Therefore the base BC coincides with the base EF , and is equal to it . [ Axiom 8 . Therefore the whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Axiom 8 . And the other angles of the one ...
Seite 11
... Axiom 3 . And FC was shewn to be equal to GB ; therefore the two sides BF , FC are equal to the two sides CG , GB , each to each ; and the angle BFC was shewn to be equal to the angle CGB ; therefore the triangles BFC , CGB are equal ...
... Axiom 3 . And FC was shewn to be equal to GB ; therefore the two sides BF , FC are equal to the two sides CG , GB , each to each ; and the angle BFC was shewn to be equal to the angle CGB ; therefore the triangles BFC , CGB are equal ...
Seite 12
... Axiom 9 . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two angles & c . Q.E.D. Corollary . Hence every equiangular triangle is also equilateral . PROPOSITION 7. THEOREM . On the same base , and on the ...
... Axiom 9 . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two angles & c . Q.E.D. Corollary . Hence every equiangular triangle is also equilateral . PROPOSITION 7. THEOREM . On the same base , and on the ...
Seite 13
... Axiom 9 . therefore the angle FDC is also greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . Again , because BC is equal to BD , the angle BDC is equal to the angle BCD . [ Hypothesis . [ I. 5 ...
... Axiom 9 . therefore the angle FDC is also greater than the angle BCD ; much more then is the angle BDC greater than the angle BCD . Again , because BC is equal to BD , the angle BDC is equal to the angle BCD . [ Hypothesis . [ I. 5 ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 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.
Seite 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.
Seite 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Seite 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.
Seite 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.
Seite 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Seite 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.
Seite 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
Seite 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.
Seite 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.