The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 páginas |
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Página 42
... right angles ; and KBC is a right angle ; wherefore GCB G H K D F E is a right angle ; and therefore also the angles ... half the line . Let the straight line AB be divided into two equal parts in the point c , and into two unequal ...
... right angles ; and KBC is a right angle ; wherefore GCB G H K D F E is a right angle ; and therefore also the angles ... half the line . Let the straight line AB be divided into two equal parts in the point c , and into two unequal ...
Página 46
... half the line , and of the square of the line between the points of section . Let the straight line AB be divided at ... right angles to AB , and make it equal to AC or CB , and join EA , EB ; through D draw ( 1.31 . ) DF parallel ...
... half the line , and of the square of the line between the points of section . Let the straight line AB be divided at ... right angles to AB , and make it equal to AC or CB , and join EA , EB ; through D draw ( 1.31 . ) DF parallel ...
Página 47
... right angle ; therefore , the square of EA is double of the square of AC : Again , because EG is equal to GF , the ... half the line bisected , and of the square of the line made up of the half and the part produced . Let the ...
... right angle ; therefore , the square of EA is double of the square of AC : Again , because EG is equal to GF , the ... half the line bisected , and of the square of the line made up of the half and the part produced . Let the ...
Página 48
... half a right angle ( 1. 32. ) : For the same reason , each of the angles CEB , EBC is half a right angle ; therefore AEB is a right angle : And because EBC is half a right angle , DBG is also ( 1.15 . ) half a right angle , for they are ...
... half a right angle ( 1. 32. ) : For the same reason , each of the angles CEB , EBC is half a right angle ; therefore AEB is a right angle : And because EBC is half a right angle , DBG is also ( 1.15 . ) half a right angle , for they are ...
Página 87
... half a right angle . 7. Given the diagonal of a square to construct it . 8. Given the base , the perpendicular height , and one of the angles at the base of a triangle , to construct it . 9. Trisect two right angles . 10. Divide a ...
... half a right angle . 7. Given the diagonal of a square to construct it . 8. Given the base , the perpendicular height , and one of the angles at the base of a triangle , to construct it . 9. Trisect two right angles . 10. Divide a ...
Otras ediciones - Ver todas
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Sin vista previa disponible - 2014 |
The First Three Books of Euclid's Elements of Geometry from the Text of Dr ... Euclid,Thomas Tate Sin vista previa disponible - 2014 |
Términos y frases comunes
ABCD adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles CAB 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 AC straight line drawn THEOR touches the circle trapezium triangle ABC twice the rectangle vertex vertical angle
Pasajes populares
Página 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...
Página 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Página 20 - If two triangles have two sides of the one equal to two sides of the...
Página 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.