The first three books of Euclid's Elements of geometry, with theorems and problems, by T. TateLongman, Brown, Green, and Longmans, 1849 - 108 páginas |
Dentro del libro
Resultados 6-10 de 12
Página 73
... semicircle : But if the angle ABD be less than BAD , the centre e falls within the segment ABC , which is therefore greater than a semicircle : Wherefore a segment of a circle being given , the circle is described of which it is a ...
... semicircle : But if the angle ABD be less than BAD , the centre e falls within the segment ABC , which is therefore greater than a semicircle : Wherefore a segment of a circle being given , the circle is described of which it is a ...
Página 76
... semicircle ; because DC passes through the centre ( III . 1. Cor . ) . Wherefore the circumference AD is equal to the circumference DB : Therefore the given circumference is bisected in D : Which was to be done . PROP . XXXI . THEOR ...
... semicircle ; because DC passes through the centre ( III . 1. Cor . ) . Wherefore the circumference AD is equal to the circumference DB : Therefore the given circumference is bisected in D : Which was to be done . PROP . XXXI . THEOR ...
Página 77
... semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semi- circle is greater than a right angle . Let ABCD be a circle , of which the ...
... semicircle is a right angle ; but the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semi- circle is greater than a right angle . Let ABCD be a circle , of which the ...
Página 78
... semicircle is a right ( III . 31. ) angle , and consequently the other two angles BAD , ABD are equal ( 1. 32. ) to a right angle : But ABF is likewise a right angle ; there- E fore the angle ABF is equal to the angles BAD , ABD : Take ...
... semicircle is a right ( III . 31. ) angle , and consequently the other two angles BAD , ABD are equal ( 1. 32. ) to a right angle : But ABF is likewise a right angle ; there- E fore the angle ABF is equal to the angles BAD , ABD : Take ...
Página 79
... semicircle AHB ; therefore the angle AHB in a semicircle is ( ш . 31. ) equal to the right angle at c . H A F B But , if the angle c be not a right angle , at the point a , in the straight line AB , make ( 1. 23. ) the angle BAD equal ...
... semicircle AHB ; therefore the angle AHB in a semicircle is ( ш . 31. ) equal to the right angle at c . H A F B But , if the angle c be not a right angle , at the point a , in the straight line AB , make ( 1. 23. ) the angle BAD equal ...
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.