The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Results 1-5 of 69
Page 3
... diameter of a circle is a straight line drawn through See N. the centre , and terminated both ways by the circum- ference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter ...
... diameter of a circle is a straight line drawn through See N. the centre , and terminated both ways by the circum- ference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter ...
Page 29
... diameter is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter : the opposite sides and angles of the figure shall be equal to one another ; and the diameter BC shall bisect it ...
... diameter is the straight line joining two of its opposite angles . Let ACDB be a parallelogram , of which BC is a diameter : the opposite sides and angles of the figure shall be equal to one another ; and the diameter BC shall bisect it ...
Page 30
... diameter bisects them : for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; and the angle ABC has been proved equal to the angle BCD ; therefore the triangle ABC is equal to the ...
... diameter bisects them : for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; and the angle ABC has been proved equal to the angle BCD ; therefore the triangle ABC is equal to the ...
Page 32
... diameter DC bisects it : but the halves of equal things are * equal ; therefore the triangle ABC is equal to the ... diameter AB bisects * it ; and the triangle DEF is the half of the parallelogram DEFH , because the diameter DF bisects ...
... diameter DC bisects it : but the halves of equal things are * equal ; therefore the triangle ABC is equal to the ... diameter AB bisects * it ; and the triangle DEF is the half of the parallelogram DEFH , because the diameter DF bisects ...
Page 34
... diameter AC divides it into two equal parts ; where- fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. * PROP . XLII . PROB . To describe a parallelogram that shall be equal to a given ...
... diameter AC divides it into two equal parts ; where- fore ABCD is also double of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. * PROP . XLII . PROB . To describe a parallelogram that shall be equal to a given ...
Other editions - View all
The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn 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