The Elements of Euclid for the Use of Schools and Colleges: With Notes, an Appendix, and Exercises. comprising the first six books and portions of the eleventh and twelfth booksMacmillan and Company, 1880 - 400 páginas |
Dentro del libro
Resultados 1-5 de 35
Página 134
... equimultiples whatever of the first and the third being taken , and any equimultiples whatever of the second and the fourth , if the multiple of the first be less than that of the second , the multiple of the third is also less than ...
... equimultiples whatever of the first and the third being taken , and any equimultiples whatever of the second and the fourth , if the multiple of the first be less than that of the second , the multiple of the third is also less than ...
Página 135
... equimultiples of four magnitudes , taken as in the fifth definition , 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 ...
... equimultiples of four magnitudes , taken as in the fifth definition , 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 ...
Página 137
... Equimultiples of the same , or of equal magnitudes , are equal to one another . 2. Those magnitudes , of which the same or equal mag- nitudes are equimultiples , are equal to one another . 3. A multiple of a greater magnitude is greater ...
... Equimultiples of the same , or of equal magnitudes , are equal to one another . 2. Those magnitudes , of which the same or equal mag- nitudes are equimultiples , are equal to one another . 3. A multiple of a greater magnitude is greater ...
Página 138
... equimultiples of as many , each of each ; whatever 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 ...
... equimultiples of as many , each of each ; whatever 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 ...
Página 139
... equal to C , so many are there in DE equal to F. For the same reason , as many magnitudes as there are in BG equal ... equimultiples , the one of the second , and the other of the fourth . Let A the first be the same multiple of B BOOK ...
... equal to C , so many are there in DE equal to F. For the same reason , as many magnitudes as there are in BG equal ... equimultiples , the one of the second , and the other of the fourth . Let A the first be the same multiple of B BOOK ...
Otras ediciones - Ver todas
The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ... Issac Todhunter Sin vista previa disponible - 2014 |
Términos y frases comunes
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC 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 225 - 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.
Página 284 - 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 73 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Página 39 - Triangles upon the same base, and between the same parallels, are equal to one another.
Página 10 - 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 353 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Página 67 - ... subtending the obtuse angle, is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle between the perpendicular and the obtuse angle, Let ABC be an obtuse-angled triangle, having the obtuse angle ACB; and from the point A, let AD be drawn perpendicular to BC produced.
Página 300 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Página xv - PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given Jinite straight line. Let AB be the given straight line. It is required to describe an equilateral triangle upon AB, From the centre A, at the distance AB, describe the circle BCD ; (post.
Página 36 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.