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 twelfth |
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Results 1-5 of 75
Page 3
... given ; and by taking out of this Book , besides other things , the good ... magnitude . " Now this Proposition is a Theorem , not a Definition ; because ... magnitude , and yet be unequal to one another , as shall be made evi- dent in ...
... given ; and by taking out of this Book , besides other things , the good ... magnitude . " Now this Proposition is a Theorem , not a Definition ; because ... magnitude , and yet be unequal to one another , as shall be made evi- dent in ...
Page 4
... with the eleventh and t Robert Simson. angles of the same number and magnitude , placed in the same order ; but neither is this universally true , except in the case in which the solid angles are contained by no more than three plane ...
... with the eleventh and t Robert Simson. angles of the same number and magnitude , placed in the same order ; but neither is this universally true , except in the case in which the solid angles are contained by no more than three plane ...
Page 252
... magnitude to itself a certain number of times ; and this is to be found in ... given the other which he blames . He says , he would not leave it out , be ... given Borellus a handle to say this of him : because when Clavius , in the above ...
... magnitude to itself a certain number of times ; and this is to be found in ... given the other which he blames . He says , he would not leave it out , be ... given Borellus a handle to say this of him : because when Clavius , in the above ...
Page 256
... with the eleventh and t Robert Simson. Euclid had given , has been deceived in applying what is manifest , when understood of magnitudes , unto ratios , viz . that a magnitude cannot be both greater and less than another . That those ...
... with the eleventh and t Robert Simson. Euclid had given , has been deceived in applying what is manifest , when understood of magnitudes , unto ratios , viz . that a magnitude cannot be both greater and less than another . That those ...
Page 270
... given rectangle C , D , exceeding by the square BP . be done . Which was to Willebrordus Snellius was the first , as ... magnitude of it being likewise given , to find its sides . And the fourth problem is the same with this . To find ...
... given rectangle C , D , exceeding by the square BP . be done . Which was to Willebrordus Snellius was the first , as ... magnitude of it being likewise given , to find its sides . And the fourth problem is the same with this . To find ...
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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.
Page 18 - ABD, the less to the greater, which is impossible ; therefore BE is not in the same straight line with BC.
Page 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.
Page 8 - Let it be granted that a straight line may be drawn from any one point to any other point.
Page 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.
Page 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.
Page 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...
Page 20 - ANY two angles of a triangle are together less than two right angles.