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 9
... bases or third sides equal ; and the two triangles shall be equal , and their other angles shall be equal , each to ... base EF , and the triangle ABC to the tri- angle DEF , and the other angles shall be equal , each to each , to which ...
... bases or third sides equal ; and the two triangles shall be equal , and their other angles shall be equal , each to ... base EF , and the triangle ABC to the tri- angle DEF , and the other angles shall be equal , each to each , to which ...
Σελίδα 10
... base BC will coincide with the base EF ; because , B coinciding with E and C with F , if the base BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Axiom 10 . Therefore the base BC ...
... base BC will coincide with the base EF ; because , B coinciding with E and C with F , if the base BC does not coincide with the base EF , two straight lines will enclose a space ; which is impossible . [ Axiom 10 . Therefore the base BC ...
Σελίδα 11
... base FC is equal to the base GB , and the triangle AFC to the triangle AGB , and the remaining angles of the one to the remaining angles of the other , each to each , to which the equal sides are opposite , B namely the angle ACF to the ...
... base FC is equal to the base GB , and the triangle AFC to the triangle AGB , and the remaining angles of the one to the remaining angles of the other , each to each , to which the equal sides are opposite , B namely the angle ACF to the ...
Σελίδα 12
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB , the less to the greater ; which is absurd . [ I. 4 . [ Axiom 9 . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two ...
... base DC is equal to the base AB , and the triangle DBC is equal to the triangle ACB , the less to the greater ; which is absurd . [ I. 4 . [ Axiom 9 . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two ...
Σελίδα 13
... base & c . Q.E.D. PROPOSITION 8. THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle which is contained by the BOOK I. 7 , 8 . 13.
... base & c . Q.E.D. PROPOSITION 8. THEOREM . If two triangles have two sides of the one equal to two sides of the other , each to each , and have likewise their bases equal , the angle which is contained by the BOOK I. 7 , 8 . 13.
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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.