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 247
... formed by drawing straight lines to touch the circle at the points E , F , G , H ; and the square thus formed is greater than the circle ; therefore the square EFGH is greater than half of the circle . Bisect the arcs EF , FG , GH , HE ...
... formed by drawing straight lines to touch the circle at the points E , F , G , H ; and the square thus formed is greater than the circle ; therefore the square EFGH is greater than half of the circle . Bisect the arcs EF , FG , GH , HE ...
Σελίδα 252
... formed by the meeting of two curved lines , or of a straight line and a curved line ; this definition however is of no importance , as the only angles ever considered are such as are formed by straight lines . The definition of a plane ...
... formed by the meeting of two curved lines , or of a straight line and a curved line ; this definition however is of no importance , as the only angles ever considered are such as are formed by straight lines . The definition of a plane ...
Σελίδα 255
... formed by the base of a triangle and the sides pro- duced be equal , the sides of the triangle are equal ; this pro- position is true and will serve as an exercise for the student . The converse of a true proposition is not necessarily ...
... formed by the base of a triangle and the sides pro- duced be equal , the sides of the triangle are equal ; this pro- position is true and will serve as an exercise for the student . The converse of a true proposition is not necessarily ...
Σελίδα 257
... formed on the other side of BC by these produced parts , and each of them would be equal to the angle BCG . The opinion has been maintained that even in I. I , it is tacitly assumed that the straight lines AC and BC cannot have a common ...
... formed on the other side of BC by these produced parts , and each of them would be equal to the angle BCG . The opinion has been maintained that even in I. I , it is tacitly assumed that the straight lines AC and BC cannot have a common ...
Σελίδα 289
... formed , and if the vertices be put on the same side of the base another solid is formed . The two solids thus formed are con tained by the same number of similar and equal plane figures , but they are not equal . It will be observed ...
... formed , and if the vertices be put on the same side of the base another solid is formed . The two solids thus formed are con tained by the same number of similar and equal plane figures , but they are not equal . It will be observed ...
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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.