The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Results 1-5 of 100
Page 9
Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . * 3 Ax , PROP . III . PROB . G * 2.1 . From the greater of two given straight lines to cut off a part equal ...
Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Which was to be done . * 3 Ax , PROP . III . PROB . G * 2.1 . From the greater of two given straight lines to cut off a part equal ...
Page 12
For , if AB be not equal to AC , one of them is greater than the other : let AB be the greater ; and from it cut * off DB equal to AC , the less , and join DC : therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC ...
For , if AB be not equal to AC , one of them is greater than the other : let AB be the greater ; and from it cut * off DB equal to AC , the less , and join DC : therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC ...
Page 13
... and the triangle DBC is equal to the triangle * ACB , the less to the D greater , which is absurd . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c . Q. E. D. B * * 4.1 . с - Cor .
... and the triangle DBC is equal to the triangle * ACB , the less to the D greater , which is absurd . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c . Q. E. D. B * * 4.1 . с - Cor .
Page 14
Again , because CB is Hyp . equalt to DB , the angle BDC is equal * to the angle BCD ; but BDC has been proved to be greater than the same BCD : which is impossible . The case in which the vertex of one triangle is upon a side of the ...
Again , because CB is Hyp . equalt to DB , the angle BDC is equal * to the angle BCD ; but BDC has been proved to be greater than the same BCD : which is impossible . The case in which the vertex of one triangle is upon a side of the ...
Page 21
If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite 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 ...
If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite 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 ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Other editions - View all
The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |
Common terms and phrases
altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole
Bibliographic information
| Title | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
| Author | Euclid |
| Editors | Robert Simson, Samuel Maynard |
| Translated by | Robert Simson |
| Publisher | Longman, Orme, Brown, Green, and Longmans, 1838 |
| Original from | University of Iowa |
| Digitized | 13 Jul 2015 |
| Length | 328 pages |
| Export Citation | BiBTeX EndNote RefMan |