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 sider |
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Side 9
... angle EDF : the base BC shall be equal to the base EF , and the triangle ABC to the tri- angle DEF , and the other angles shall be equal , each to each , to which the equal B sides are opposite , namely , the angle ABC to the angle DEF ...
... angle EDF : the base BC shall be equal to the base EF , and the triangle ABC to the tri- angle DEF , and the other angles shall be equal , each to each , to which the equal B sides are opposite , namely , the angle ABC to the angle DEF ...
Side 10
... angle BAĆ is equal to the angle EDF . B [ Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with the point E , therefore the base BC ...
... angle BAĆ is equal to the angle EDF . B [ Hypothesis . Therefore also the point C will coincide with the point F , because AC is equal to DF . [ Hypothesis . But the point B was shewn to coincide with the point E , therefore the base BC ...
Side 14
... angle BÁC shall be equal to the angle EDF . D G B. E For if the triangle ABC be applied to the triangle DEF , so that the point B may be on the point E , and the straight line BC on the straight line EF , the point C will also coin ...
... angle BÁC shall be equal to the angle EDF . D G B. E For if the triangle ABC be applied to the triangle DEF , so that the point B may be on the point E , and the straight line BC on the straight line EF , the point C will also coin ...
Side 26
... angle equal to a given rectilineal angle . Let AB be the given straight line , and A the given point in it , and DCE ... EDF : the base BC shall be greater than the base EF . Of the two sides 26 EUCLID'S ELEMENTS .
... angle equal to a given rectilineal angle . Let AB be the given straight line , and A the given point in it , and DCE ... EDF : the base BC shall be greater than the base EF . Of the two sides 26 EUCLID'S ELEMENTS .
Side 28
... angle contained by the sides equal to them , of the other . Let ABC , DEF be two triangles , which have the two ... EDF . For if not , the angle BAC must be either equal to the angle EDF or less than the angle EDF . But the angle BAC is ...
... angle contained by the sides equal to them , of the other . Let ABC , DEF be two triangles , which have the two ... EDF . For if not , the angle BAC must be either equal to the angle EDF or less than the angle EDF . But the angle BAC is ...
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Almindelige termer og sætninger
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
Populære passager
Side 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.
Side 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.
Side 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Side 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.
Side 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.
Side 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Side 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.
Side 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
Side 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.
Side 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.