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 σελίδες |
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Αποτελέσματα 1 - 5 από τα 41.
Σελίδα 251
... given in its proper place instead of this corollary ; and another corollary ... position , it is required that EB may be the same multiple of CG , that AE ... given the BOOK V. 251 NOTES .
... given in its proper place instead of this corollary ; and another corollary ... position , it is required that EB may be the same multiple of CG , that AE ... given the BOOK V. 251 NOTES .
Σελίδα 266
... position : but in this the author neglects permutation , and does not show ... given of this proposition has been vitiated by some unskilful hand : for ... position , viz . the third of four proportionals is equal to the fourth , if the ...
... position : but in this the author neglects permutation , and does not show ... given of this proposition has been vitiated by some unskilful hand : for ... position , viz . the third of four proportionals is equal to the fourth , if the ...
Σελίδα 270
... given rectangle C , D , exceeding by the square BP . be done . Which was to ... given straight line AB in the point N , so as to make the rectangle AN , NB equal ... position was needful : and the 32d may be otherwise and something more ...
... given rectangle C , D , exceeding by the square BP . be done . Which was to ... given straight line AB in the point N , so as to make the rectangle AN , NB equal ... position was needful : and the 32d may be otherwise and something more ...
Σελίδα 287
... position necessarily requires . The demonstration of the proposition is spoiled and mutilated ; for some easy things ... given , it was thought proper to give it , and to demonstrate , that the pyramids in it are similar to those of the ...
... position necessarily requires . The demonstration of the proposition is spoiled and mutilated ; for some easy things ... given , it was thought proper to give it , and to demonstrate , that the pyramids in it are similar to those of the ...
Σελίδα 293
... given , and the ratios of their sides given . IV . Points , lines , and spaces , are said to be given in position , which have always the same situation , and which are either actually exhibited , or can be found . A. An angle is said to be ...
... given , and the ratios of their sides given . IV . Points , lines , and spaces , are said to be given in position , which have always the same situation , and which are either actually exhibited , or can be found . A. An angle is said to be ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Σελίδα 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.
Σελίδα 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 20 - ANY two angles of a triangle are together less than two right angles.