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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Page 3
... Greek editions we now have , I found that Theon , or whoever was the editor of the present Greek text , by adding some things , suppressing others , and mixing his own with Euclid's Demonstrations , had changed more things to the worse ...
... Greek editions we now have , I found that Theon , or whoever was the editor of the present Greek text , by adding some things , suppressing others , and mixing his own with Euclid's Demonstrations , had changed more things to the worse ...
Page 64
... Greek text , and translations from it , the angle of the semi- H A Ꭰ circle is said to be greater than any acute rectilineal angle , and the remaining angle less than any rectilineal angle . ' COR . From this it is manifest , that the ...
... Greek text , and translations from it , the angle of the semi- H A Ꭰ circle is said to be greater than any acute rectilineal angle , and the remaining angle less than any rectilineal angle . ' COR . From this it is manifest , that the ...
Page 73
... Greek text , and the translations from it , the angle of the greater segment is said to be greater , and the angle of the less segment is said to be less , than a right angle . " COR . From this it is manifest , that if one angle of a ...
... Greek text , and the translations from it , the angle of the greater segment is said to be greater , and the angle of the less segment is said to be less , than a right angle . " COR . From this it is manifest , that if one angle of a ...
Page 216
... Greek , because the pyramid , in what follows , is supposed to be circumscribed about the cone , and so must have the same vertex . And the same change is made in some places following . equal parts in the points O , P , R 216 BOOK XII ...
... Greek , because the pyramid , in what follows , is supposed to be circumscribed about the cone , and so must have the same vertex . And the same change is made in some places following . equal parts in the points O , P , R 216 BOOK XII ...
Page 235
... GREEK TEXT ; AND THE REASONS OF THE ALTERATIONS WHICH HAVE BEEN MADE . AS ALSO OBSERVATIONS ON SOME OF THE PROPOSITIONS . BY ROBERT SIMSON , M. D. EMERITUS PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF GLASGOW . NOTES , & c . DEFINITION ...
... GREEK TEXT ; AND THE REASONS OF THE ALTERATIONS WHICH HAVE BEEN MADE . AS ALSO OBSERVATIONS ON SOME OF THE PROPOSITIONS . BY ROBERT SIMSON , M. D. EMERITUS PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF GLASGOW . NOTES , & c . DEFINITION ...
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.