The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Page 14
... produce AC , AD to E , F Hyp . therefore , because AC is equal † to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal to one another : but the 19 Ax . angle ECD is greater than the angle BCD ...
... produce AC , AD to E , F Hyp . therefore , because AC is equal † to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal to one another : but the 19 Ax . angle ECD is greater than the angle BCD ...
Page 17
... produced to any length both ways , and let C be a point with- out it . It is required to draw a straight line perpendicular to AB from the point C. Take any point D upon the H B other side of AB , and from the centre C c 3 BOOK I. PROP ...
... produced to any length both ways , and let C be a point with- out it . It is required to draw a straight line perpendicular to AB from the point C. Take any point D upon the H B other side of AB , and from the centre C c 3 BOOK I. PROP ...
Page 21
... produced , the exterior angle is greater than either of the interior op- posite angles .. Let ABC be a triangle , and let its side BC be produced to D : the exterior angle ACD shall be greater than either of the interior opposite angles ...
... produced , the exterior angle is greater than either of the interior op- posite angles .. Let ABC be a triangle , and let its side BC be produced to D : the exterior angle ACD shall be greater than either of the interior opposite angles ...
Page 22
... Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , * 16 1. ACD is greater than the in- terior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles 14 Ax . ACD , ACB are greater ...
... Produce BC to D ; and be- cause ACD is the exterior angle of the triangle ABC , * 16 1. ACD is greater than the in- terior and opposite angle ABC ; to each of these add the angle ACB ; therefore the angles 14 Ax . ACD , ACB are greater ...
Page 23
... Produce BA to the point D , and make * AD equal to AC ; and join DC . Because DA is equal to AC , the angle ADC is equal * to ACD ; but the angle B D 18. 1 . * 3.1 . * 5.1 . BCD is greater than the angle ACD : there- † 9 Ax . fore the ...
... Produce BA to the point D , and make * AD equal to AC ; and join DC . Because DA is equal to AC , the angle ADC is equal * to ACD ; but the angle B D 18. 1 . * 3.1 . * 5.1 . BCD is greater than the angle ACD : there- † 9 Ax . fore the ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole