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 O F Euclid's Data in Like Manner CorrectedF. Wingrave, 1809 - 531 σελίδες |
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Αποτελέσματα 1 - 5 από τα 99.
Σελίδα 8
... less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw the straight line AD equal to C ; and from the ...
... less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part equal to C , the less . From the point A draw the straight line AD equal to C ; and from the ...
Σελίδα 11
... less , and join DC ; there fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both the two sides , DB , BC are equal to the two AC , CB each to each ; and the angle DBC is equal to the angle ACB ; therefore ...
... less , and join DC ; there fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both the two sides , DB , BC are equal to the two AC , CB each to each ; and the angle DBC is equal to the angle ACB ; therefore ...
Σελίδα 19
... less than two right angles . In like manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII . THEOR . THE greater side of every ...
... less than two right angles . In like manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROP . XVIII . THEOR . THE greater side of every ...
Σελίδα 20
... less than the angle ACB ; but it is not ; therefore the side AC is not less than AB ; and it has been shown that 18. 1. it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX ...
... less than the angle ACB ; but it is not ; therefore the side AC is not less than AB ; and it has been shown that 18. 1. it is not equal to AB ; therefore AC is greater than AB . Wherefore the greater angle , & c . Q. E. D. PROP . XX ...
Σελίδα 24
... less ; because then the base BC would b 24. 1. be less than the base EF ; but it is not ; there- fore the angle BAC is B D E not less than the angle EDF ; and it was shown that it is not equal to it ; therefore the angle BAC is greater ...
... less ; because then the base BC would b 24. 1. be less than the base EF ; but it is not ; there- fore the angle BAC is B D E not less than the angle EDF ; and it was shown that it is not equal to it ; therefore the angle BAC is greater ...
Άλλες εκδόσεις - Προβολή όλων
The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABC circumference common logarithm cone cylinder demonstrated described diameter 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 logarithm multiple opposite parallel parallelogram 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 parallelopipeds square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC triplicate ratio vertex