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 63
Euclid, Thomas Tate. PROP . XII . THEOR . If two circles touch each other externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ABC , ADE touch each other externally in the ...
Euclid, Thomas Tate. PROP . XII . THEOR . If two circles touch each other externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ABC , ADE touch each other externally in the ...
Página 67
... circle : For , if possible , let FA be between them , and from the point D draw ( 1. 12. ) DG perpendicular to FA ... touches the circle ; and that it touches it only in one point , because , if it did meet the circle in two , it would ...
... circle : For , if possible , let FA be between them , and from the point D draw ( 1. 12. ) DG perpendicular to FA ... touches the circle ; and that it touches it only in one point , because , if it did meet the circle in two , it would ...
Página 68
... touches the circle ( m . 16. Cor . ) . PROP . XVIII . THEOR . If a straight line touches a circle , the straight line drawn from the centre to the point of contact , shall be perpendicular to the line touching the circle . Let the ...
... touches the circle ( m . 16. Cor . ) . PROP . XVIII . THEOR . If a straight line touches a circle , the straight line drawn from the centre to the point of contact , shall be perpendicular to the line touching the circle . Let the ...
Página 69
... touch the circle ABC in C , and from C let CA be drawn at right angles to DE ; the centre of the circle is in CA. A For , if not , let F be the centre , if possible , and join CF. Because DE touches the circle ABC , and FC is drawn from ...
... touch the circle ABC in C , and from C let CA be drawn at right angles to DE ; the centre of the circle is in CA. A For , if not , let F be the centre , if possible , and join CF. Because DE touches the circle ABC , and FC is drawn from ...
Página 78
... touches a circle , and from the point of contact a straight line be drawn cutting the circle , the angles made by this line with the line touching the circle , shall be equal to the angles which are in the alternate segments of the circle ...
... touches a circle , and from the point of contact a straight line be drawn cutting the circle , the angles made by this line with the line touching the circle , shall be equal to the angles which are in the alternate segments of the circle ...
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 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
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.