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, 1883 - 400 sider |
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Side 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 ...
Side 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 ...
Side 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 ...
Side 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 ...
Side 139
... equal to C , so many are there in DE equal to F. For the same reason , as many magnitudes as there are in BĞ 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 BĞ equal ... equimultiples , the one of the second , and the other of the fourth . Let A the first be the same multiple of B BOOK ...
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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
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Side 262 - 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.
Side 71 - 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.
Side 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Side 182 - 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.
Side 8 - 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.
Side 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Side 58 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Side 60 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB
Side 242 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.
Side 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.