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 páginas |
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Página 134
... multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a ... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ...
... multiple of a less , when the greater is measured by the less ; that is , when the greater contains the less a ... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth ...
Página 135
... multiple of the first is greater than the multiple of the second , but the multiple of the third is not greater than the multiple of the fourth , then the first is said to have to the second a greater ratio than the third has to the ...
... multiple of the first is greater than the multiple of the second , but the multiple of the third is not greater than the multiple of the fourth , then the first is said to have to the second a greater ratio than the third has to the ...
Página 137
... multiple of a greater magnitude is greater than the same multiple of a less . 4. That magnitude , of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION 1. THEOREM . If any ...
... multiple of a greater magnitude is greater than the same multiple of a less . 4. That magnitude , of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROPOSITION 1. THEOREM . If any ...
Página 138
... multiple any one of them is of its part , the same multiple shall all the first magni- tudes be of all the other . Let any number of magnitudes AB , CD be equimul- tiples of as many others E , F , each of each : whatever multiple AB is ...
... multiple any one of them is of its part , the same multiple shall all the first magni- tudes be of all the other . Let any number of magnitudes AB , CD be equimul- tiples of as many others E , F , each of each : whatever multiple AB is ...
Página 139
... multiple of C the second , that DE the third is of F the fourth , and let BG the fifth be the same multiple of C the second , that EH the sixth is of F the fourth : AG , the first together with the fifth , shall be the same multiple of ...
... multiple of C the second , that DE the third is of F the fourth , and let BG the fifth be the same multiple of C the second , that EH the sixth is of F the fourth : AG , the first together with the fifth , shall be the same multiple of ...
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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...
Página 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...
Página 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.
Página 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.
Página 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Página 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.
Página 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.
Página 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.
Página 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.