The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 3
A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter .
A diameter of a circle is a straight line drawn through the centre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the circumference cut off by the diameter .
Page 36
The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . N.B. – A parallelogram is a four - sided figure , of which the opposite sides are ...
The opposite sides and angles of parallelograms are equal to one another , and the diameter bisects them , that is , divides them into two equal parts . N.B. – A parallelogram is a four - sided figure , of which the opposite sides are ...
Page 37
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 triangle BCD , and the diameter * 4 . 1 . BC divides the parallelogram ACDB into two equal ...
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 triangle BCD , and the diameter * 4 . 1 . BC divides the parallelogram ACDB into two equal ...
Page 39
L DBC is the half of the parallelogram DBCF , because the diameter DC bisects it : but the halves of equal things are * equal ; therefore the * ? Ak , triangle ABC is equal to the triangle DBC Wherefore triangles , & c .
L DBC is the half of the parallelogram DBCF , because the diameter DC bisects it : but the halves of equal things are * equal ; therefore the * ? Ak , triangle ABC is equal to the triangle DBC Wherefore triangles , & c .
Page 40
is the half of the parallelogram DEFH , because the diameter DF bisects it : but the halves of * 7 Ax . equal things are * equal : therefore the triangle ABC is equal to the triangle DEF . Wherefore triangles , & c . Q. E. D. ' * 37 .
is the half of the parallelogram DEFH , because the diameter DF bisects it : but the halves of * 7 Ax . equal things are * equal : therefore the triangle ABC is equal to the triangle DEF . Wherefore triangles , & c . Q. E. D. ' * 37 .
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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 |