Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J. Pryde. [With] Key1860 |
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Página 67
... those that have equal radii ; and concentric circles are those that have a common centre , c . 12. A straight line is said to touch a circle , or to be a tangent to it , when it meets the circle , and THIRD BOOK, DEFINITIONS,
... those that have equal radii ; and concentric circles are those that have a common centre , c . 12. A straight line is said to touch a circle , or to be a tangent to it , when it meets the circle , and THIRD BOOK, DEFINITIONS,
Página 68
... touch one another when they meet , but do not cut one another . Such circles may be called tangent circles . 14. The point in which a tangent and a circle , or two tangent circles , meet , is called the point of contact ; c , c , c ...
... touch one another when they meet , but do not cut one another . Such circles may be called tangent circles . 14. The point in which a tangent and a circle , or two tangent circles , meet , is called the point of contact ; c , c , c ...
Página 71
... touch another internally , the circles shall not have the same centre . which touch internally Given the two circles ABC and CDE in the point C ; to prove that they have not the same centre . ( Const . ) For , if they can , let it be F ...
... touch another internally , the circles shall not have the same centre . which touch internally Given the two circles ABC and CDE in the point C ; to prove that they have not the same centre . ( Const . ) For , if they can , let it be F ...
Página 75
... touch each other internally , the straight line which joins their centres being produced , shall pass through the point of contact . Given the two circles ABC , ADE touching each other internally in the point A , and let F be the centre ...
... touch each other internally , the straight line which joins their centres being produced , shall pass through the point of contact . Given the two circles ABC , ADE touching each other internally in the point A , and let F be the centre ...
Página 76
... touch the circle ABC in more points than one , the points B and D ; BD at right angles ( I. 10 , 11 ) ; ( Dem ... touch another on the inside in more points than one . Nor can two circles touch one another externally in more than for ...
... touch the circle ABC in more points than one , the points B and D ; BD at right angles ( I. 10 , 11 ) ; ( Dem ... touch another on the inside in more points than one . Nor can two circles touch one another externally in more than for ...
Otras ediciones - Ver todas
Euclid's Elements of Plane Geometry [Book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Sin vista previa disponible - 2023 |
Euclid's Elements of Plane Geometry [book 1-6] Explicitly Enunciated, by J ... Euclides,James Pryde Sin vista previa disponible - 2018 |
Términos y frases comunes
ABCD adjacent angles angle ABC angle ACB angle BAC apothem BA and AC base BC BC is equal bisected centre Chambers's chord circle ABC circumference Const cosec cosine described diameter divided double draw equal angles equal to twice equiangular equilateral polygon equimultiples exterior angle fore given line given point given straight line gnomon greater hence hypotenuse inscribed isosceles triangle less line drawn multiple number of sides opposite angle parallel parallelogram perimeter perpendicular polygon produced proportional PROPOSITION prove radius ratio rectangle contained rectilineal figure regular polygon remaining angle right angles right-angled triangle segment semiperimeter shewn similar sine square on AC straight line AC tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertical angle wherefore
Pasajes populares
Página 23 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Página 52 - If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced.
Página 51 - If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Página 53 - If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC...
Página 3 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Página 29 - Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 117 - And the same thing is to be understood when it is more briefly expressed by saying, a has to d the ratio compounded of the ratios of e to f, g to h, and k to l. In like manner, the same things being supposed, if m has to n the same ratio which a has to d ', then, for shortness...
Página 13 - 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 159 - From the point A draw a straight line AC, making any angle with AB ; and in AC take any point D, and take AC the same multiple of AD, that AB is of the part which is to be cut off from it : join BC, and draw DE parallel to it : then AE is the part required to be cut off. Because ED is parallel to one of the sides of the triangle ABC, viz. to BC ; as CD is to DA, so is (2.
Página 60 - CB, BA, by twice the rectangle CB, BD. Secondly, Let AD fall without the triangle ABC. Then, because the angle at D is a right angle, the angle ACB is greater than a right angle ; (i.