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 Exercises |
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Page ix
... take up Logic before Geometry ; and it seems therefore premature to devote space to a subject which will be altogether unsuitable to the majority of those who use a work like the present . After the notes will be found an Appendix ...
... take up Logic before Geometry ; and it seems therefore premature to devote space to a subject which will be altogether unsuitable to the majority of those who use a work like the present . After the notes will be found an Appendix ...
Page 10
... ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater cut off AG equal to AF the less , [ I.3 . 1 and join FC , GB . Because A Fis equal 10 EUCLID'S ELEMENTS .
... ABC shall be equal to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater cut off AG equal to AF the less , [ I.3 . 1 and join FC , GB . Because A Fis equal 10 EUCLID'S ELEMENTS .
Page 15
... Take any point D in AB , and from AC cut off AE equal to AD ; [ I. 3 . join DE , and on DE , on the side remote from A , describe the equi- lateral triangle DEF . [ I. 1 . B Join AF . The straight line AF shall bisect the angle BAC ...
... Take any point D in AB , and from AC cut off AE equal to AD ; [ I. 3 . join DE , and on DE , on the side remote from A , describe the equi- lateral triangle DEF . [ I. 1 . B Join AF . The straight line AF shall bisect the angle BAC ...
Page 16
... Take any point D in AC , and make CE equal to CD . [ I. 3 . On DE describe the equilateral triangle DFE , and join CF. [ I. 1 . The straight line CF drawn from the given point C shall be at right angles to the given straight line AB ...
... Take any point D in AC , and make CE equal to CD . [ I. 3 . On DE describe the equilateral triangle DFE , and join CF. [ I. 1 . The straight line CF drawn from the given point C shall be at right angles to the given straight line AB ...
Page 17
... Take any point D on the other side of AB , and from the centre C , at the distance CD , describe the circle EGF , meeting AB at F and G. [ Postulate 3 . Bisect FG at H , and join CH . [ I. 10 . E H B D The straight line CH drawn from ...
... Take any point D on the other side of AB , and from the centre C , at the distance CD , describe the circle EGF , meeting AB at F and G. [ Postulate 3 . Bisect FG at H , and join CH . [ I. 10 . E H B D The straight line CH drawn from ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 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...
Page 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...
Page 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.
Page 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.
Page 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Page 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.
Page 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.
Page 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.
Page 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.