The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 2
D V L BY 6 6 -CE N.B. “ When several angles are at one point ' B , any one of them is expressed by three let- ' ters , of which the letter that is at the vertex of the angle , that is , at the point in which the straight lines that ...
D V L BY 6 6 -CE N.B. “ When several angles are at one point ' B , any one of them is expressed by three let- ' ters , of which the letter that is at the vertex of the angle , that is , at the point in which the straight lines that ...
Page 13
... in the case in which the vertex of each of the triangles is without the other triangle , because AC is equal t to A R + Hyp . AD , the angle ACD is equal * to the angle ADC : But the angle ACD is greater t +9 Ax . than the angle BCD ...
... in the case in which the vertex of each of the triangles is without the other triangle , because AC is equal t to A R + Hyp . AD , the angle ACD is equal * to the angle ADC : But the angle ACD is greater t +9 Ax . than the angle BCD ...
Page 14
But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F. + Hyp . therefore , because AC is ... The case in which the vertex of one triangle is upon a side of the other , needs nodemonstration .
But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F. + Hyp . therefore , because AC is ... The case in which the vertex of one triangle is upon a side of the other , needs nodemonstration .
Page 34
... are sides of the figure : and the same angles are equal to the angles of the figure , together with the angles at the point F , which is the common vertex of the triangles ; * 2 Cor . that is , * together with four right angles .
... are sides of the figure : and the same angles are equal to the angles of the figure , together with the angles at the point F , which is the common vertex of the triangles ; * 2 Cor . that is , * together with four right angles .
Page 168
The altitude of any figure is the straight line drawn from its vertex perpendicular to the base . > PROP . I. THEOR . Triangles and parallelograms of the same altitude are one to another as their bases .
The altitude of any figure is the straight line drawn from its vertex perpendicular to the base . > PROP . I. THEOR . Triangles and parallelograms of the same altitude are one to another as their bases .
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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 |