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 10
Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore the base FC is * 4.1 . equal to the base GB ...
Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two triangles AFC , AGB ; therefore the base FC is * 4.1 . equal to the base GB ...
Seite 13
Because AD is equal to AE , and AF is common to the two triangles DAF , DX E EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; and the base DF is equal to the base F C 18.1 . EF ; therefore the angle DAF ...
Because AD is equal to AE , and AF is common to the two triangles DAF , DX E EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; and the base DF is equal to the base F C 18.1 . EF ; therefore the angle DAF ...
Seite 14
Book I. Because AC is equal to CB , and CDC common to the two triangles ACD , BCD ; the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is equal to the angle BCD ; therefore the base AD is equal 4.
Book I. Because AC is equal to CB , and CDC common to the two triangles ACD , BCD ; the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is equal to the angle BCD ; therefore the base AD is equal 4.
Seite 15
Because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base CF is equald to the base CG ; therefore the angle CHF is equal o 15 Pef .
Because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base CF is equald to the base CG ; therefore the angle CHF is equal o 15 Pef .
Seite 17
Take away the common angle AED , and the reinaining angle CEA is equalb to the remaining angle DEB . In the same 3 As , manner it can be demonstrated , that the angles CEB , AED are equal . Therefore , if two straight lines , & c .
Take away the common angle AED , and the reinaining angle CEA is equalb to the remaining angle DEB . In the same 3 As , manner it can be demonstrated , that the angles CEB , AED are equal . Therefore , if two straight lines , & c .
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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
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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 |