The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthDesilver, Thomas & Company, 1838 - 416 sider |
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Side 93
... proportionals . * See Note . " N. B. When four magnitudes are proportionals , it THE ...
... proportionals . * See Note . " N. B. When four magnitudes are proportionals , it THE ...
Side 94
... proportionals , it is usually ex- pressed by saying , the first is to the second , as the third to the fourth ... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When ...
... proportionals , it is usually ex- pressed by saying , the first is to the second , as the third to the fourth ... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When ...
Side 95
... proportionals . ' XIII . Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is inferred , that the first has the same ratio to the third , which the second has to ...
... proportionals . ' XIII . Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is inferred , that the first has the same ratio to the third , which the second has to ...
Side 101
... than it , the third can be proved to be equal to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. * See Notes . PROP . B. THEOR . Ir four magnitudes be proportionals BOOK V. 101 THE ELEMENTS OF EUCLID .
... than it , the third can be proved to be equal to the fourth , or less than it . Therefore , if the first , & c . Q. E. D. * See Notes . PROP . B. THEOR . Ir four magnitudes be proportionals BOOK V. 101 THE ELEMENTS OF EUCLID .
Side 102
... proportionals they are poportionals also when taken inversely . * If the magnitude A be to B , as C is to D , then also inversely B is to A , as D , to C. Take of B and D any equimultiples whatever E and F ; and of A and C any ...
... proportionals they are poportionals also when taken inversely . * If the magnitude A be to B , as C is to D , then also inversely B is to A , as D , to C. Take of B and D any equimultiples whatever E and F ; and of A and C any ...
Vanlige uttrykk og setninger
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference Co-S cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 45 - Ir 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 41 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Side 54 - Ir any two points be taken in the circumference of a circle, the straight line which joins them shall fall within the circle. Let ABC be a circle, and A, B any two points in the circumference ; the straight line drawn from A to B shall fall within the circle.
Side 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Side 10 - From a given point to draw a straight line equal to a given straight line. Let A be the given point, and BC the given straight line: it is required to draw from the point A a straight line equal to BC.
Side 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 256 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Side 129 - 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 23 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Side 20 - ANY two angles of a triangle are together less than two right angles.