The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth ... Also the Book of Euclid's Data, in Like Manner Corrected |
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Seite 8
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 , A * 2. 1 . PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the ...
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 , A * 2. 1 . PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the ...
Seite 9
Wherefore the whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ...
Wherefore the whole triangle ABC shall coincide with the whole triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ...
Seite 13
EF ; therefore the angle DAF is equal to the angle EAF ; wherefore the given rectilineal angle BAC is bisected by the straight line AF . Which was to be done . 3 PROP . X. PROB . To bisect a given finite straight line , that is ...
EF ; therefore the angle DAF is equal to the angle EAF ; wherefore the given rectilineal angle BAC is bisected by the straight line AF . Which was to be done . 3 PROP . X. PROB . To bisect a given finite straight line , that is ...
Seite 17
And , in like manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR .
And , in like manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q. E. D. PROP . XV . THEOR .
Seite 25
... and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle ...
... and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE ; but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle ...
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ABCD added altitude angle ABC angle BAC base Book centre circle circle ABC circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn Edition equal equiangular equimultiples excess fore four fourth given angle given in magnitude given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane Price produced PROP proportionals proposition proved pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle space sphere square square of BC Take taken THEOR third triangle ABC wherefore whole
Beliebte Passagen
Seite 41 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Seite 180 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Seite 166 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides. DH Let BC, CG be placed in a straight line ; therefore DC and CE are also in a straight line (14.
Seite 2 - A rhomboid, is that which has its opposite sides equal to one another, but all its sides are not equal, nor its angles right angles.
Seite 105 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth ; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth...
Seite 79 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Seite 1 - A straight line is that which lies evenly between its extreme points.
Seite 149 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 23 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Seite 83 - Wherefore from the given circle ABC has been cut off the segment BAC, containing an angle equal to the given angle DQEP PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by the segments of the other. Let the...
Bibliografische Informationen
| Titel | The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth ... Also the Book of Euclid's Data, in Like Manner Corrected |
| Autor/in | Euclides |
| Herausgeber | Robert Simson |
| Ausgabe | 17 |
| Verlag | Wingrave and Collingwood, 1816 |
| Original von | Universität Complutense Madrid |
| Digitalisiert | 20. Mai 2008 |
| Länge | 528 Seiten |
| Zitat exportieren | BiBTeX EndNote RefMan |