The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 Seiten |
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Seite 9
... take any point F , and from AE , the greater , cut off AG equal ( 1. 3. ) to AF , the less , and join FC , GB . B G E Because AF is equal to AG , and AB to AC ( Hyp . ) , the two sides FA , AC are equal to the two GA , AB , each to each ...
... take any point F , and from AE , the greater , cut off AG equal ( 1. 3. ) to AF , the less , and join FC , GB . B G E Because AF is equal to AG , and AB to AC ( Hyp . ) , the two sides FA , AC are equal to the two GA , AB , each to each ...
Seite 12
... Take any point D in AB , and from AC cut ( 1. 3. ) off a E equal to AD ; join DE , and upon it , on the side towards B and C , describe ( 1. 1. ) an equilateral triangle DEF ; then join AF ; the straight line AF bisects the triangle BA ...
... Take any point D in AB , and from AC cut ( 1. 3. ) off a E equal to AD ; join DE , and upon it , on the side towards B and C , describe ( 1. 1. ) an equilateral triangle DEF ; then join AF ; the straight line AF bisects the triangle BA ...
Seite 13
... Take any point D in AD , and ( 1. 3. ) make CE equal to CD , and upon DE describe ( 1. 1. ) the equi- lateral triangle DFE , and join FC ; the straight line FC drawn from the given point c is at right angles to the given straight line ...
... Take any point D in AD , and ( 1. 3. ) make CE equal to CD , and upon DE describe ( 1. 1. ) the equi- lateral triangle DFE , and join FC ; the straight line FC drawn from the given point c is at right angles to the given straight line ...
Seite 14
... Take any point D upon the other side of AB , and from the centre C , at the distance CD , describe ( Post . 3. ) the circle EGF meeting AB in F , G ; and bisect ( 1. 10. ) FG in H , and join CF , CH , CG ; the straight line CH , drawn ...
... Take any point D upon the other side of AB , and from the centre C , at the distance CD , describe ( Post . 3. ) the circle EGF meeting AB in F , G ; and bisect ( 1. 10. ) FG in H , and join CF , CH , CG ; the straight line CH , drawn ...
Seite 15
... Take away the common angle ABC , the remaining angle ABE is equal ( Ax . 3. ) to the remaining angle ABD , the less to the greater , which is im- possible ; therefore BE is not in the same straight line with BC . And , in like manner ...
... Take away the common angle ABC , the remaining angle ABE is equal ( Ax . 3. ) to the remaining angle ABD , the less to the greater , which is im- possible ; therefore BE is not in the same straight line with BC . And , in like manner ...
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The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Keine Leseprobe verfügbar - 2014 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Keine Leseprobe verfügbar - 2014 |
Häufige Begriffe und Wortgruppen
ABCD adjacent angles angle ABC angle ACB angle AGH angle BAC angle BCD angle CAB angle EDF angle equal angles CBA base BC BC is equal bisect centre circle ABC circumference diameter divided double draw a straight equal angles equal circles equal straight lines equal to FB exterior angle fore given point given rectilineal angle given straight line gnomon greater half a right hypotenuse isosceles triangle less Let ABC Let the straight line be drawn opposite angles parallel parallelogram perpendicular PROB produced Q. E. D. PROP rectangle AE rectangle contained rectilineal figure remaining angle right angles segment semicircle side BC square of AC straight line AB straight line AC straight line drawn THEOR touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle
Beliebte Passagen
Seite 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Seite 20 - If two triangles have two sides of the one equal to two sides of the...
Seite 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Seite 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.
Seite 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets it shall touch the circle.
Seite 82 - If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Seite 11 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Seite 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.
Seite 7 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.