The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. 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 |
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Page 8
... similar solid figures are those which are contained by similar planes of the same number and magnitude . " Now this Proposition is a Theo- rem , not a Definition ; because the equality of figures of any kind must be demonstrated , and ...
... similar solid figures are those which are contained by similar planes of the same number and magnitude . " Now this Proposition is a Theo- rem , not a Definition ; because the equality of figures of any kind must be demonstrated , and ...
Page 9
... similar plane figures , which are not similar to one another , in the true sense of simi- larity received by all geometers ; and all these Propositions have , for these reasons , been insufficiently demonstrated since Theon's time ...
... similar plane figures , which are not similar to one another , in the true sense of simi- larity received by all geometers ; and all these Propositions have , for these reasons , been insufficiently demonstrated since Theon's time ...
Page 66
... Similar segments of a circle , are those in which the angles are equal , or which contain equal angles . D PROP . I. PROB . To find the centre of a given circle . * Let ABC be the given circle ; it is required to find its centre . Draw ...
... Similar segments of a circle , are those in which the angles are equal , or which contain equal angles . D PROP . I. PROB . To find the centre of a given circle . * Let ABC be the given circle ; it is required to find its centre . Draw ...
Page 85
... similar segments of circles , not coinciding with one another . * D Ifit be possible , let the two similar segments of circles , viz . ACB , ABD be upon the same side of the same straight line AB , not coinciding with one another : then ...
... similar segments of circles , not coinciding with one another . * D Ifit be possible , let the two similar segments of circles , viz . ACB , ABD be upon the same side of the same straight line AB , not coinciding with one another : then ...
Page 86
... similar segments , & c . Q. E. D. PROP . XXV . PROB . A SEGMENT of a circle being given to describe the circle of which it is the segment . * Let ABC be the given segment of a circle ; it is required to describe the circle of which it ...
... similar segments , & c . Q. E. D. PROP . XXV . PROB . A SEGMENT of a circle being given to describe the circle of which it is the segment . * Let ABC be the given segment of a circle ; it is required to describe the circle of which it ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |
Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference 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 gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition 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 parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore