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, 1867 - 400 σελίδες |
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Σελίδα 11
... GCB , 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.
... GCB , 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.
Σελίδα 12
... 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 base equal to one ...
... 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 base equal to one ...
Σελίδα 115
... equiangular to a given triangle . Let ABC be the given circle , and DEF the given triangle : it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF . Draw the straight line GAH touching the circle at the ...
... equiangular to a given triangle . Let ABC be the given circle , and DEF the given triangle : it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF . Draw the straight line GAH touching the circle at the ...
Σελίδα 116
... equiangular to the triangle DEF . Produce EF both ways to the points G , H ; take K the centre of the circle ABC ; [ III . 1 . from K draw any radius KB ; at the point K , in the straight line KB , make the angle BKA equal to the angle ...
... equiangular to the triangle DEF . Produce EF both ways to the points G , H ; take K the centre of the circle ABC ; [ III . 1 . from K draw any radius KB ; at the point K , in the straight line KB , make the angle BKA equal to the angle ...
Σελίδα 117
... equiangular to the tri- angle DEF , and it is described about the circle ABC . Q.E.F. PROPOSITION 4. PROBLEM . To inscribe a circle in a given triangle . Let ABC be the given triangle : it is required to inscribe a circle in the ...
... equiangular to the tri- angle DEF , and it is described about the circle ABC . Q.E.F. PROPOSITION 4. PROBLEM . To inscribe a circle in a given triangle . Let ABC be the given triangle : it is required to inscribe a circle in the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal 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
Δημοφιλή αποσπάσματα
Σελίδα 286 - 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.
Σελίδα 30 - 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. either the sides adjacent to the equal...
Σελίδα 34 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Σελίδα 37 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Σελίδα 12 - 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.
Σελίδα 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Σελίδα 220 - If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 354 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.
Σελίδα 104 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.