The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed1855 |
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Página 54
... touch a circle , when it meets the circum- ference , and being produced does not cut the circle , that is , does not intersect the circumference . If a straight line touch a circle in the sense thus defined , it is called a tangent ( ...
... touch a circle , when it meets the circum- ference , and being produced does not cut the circle , that is , does not intersect the circumference . If a straight line touch a circle in the sense thus defined , it is called a tangent ( ...
Página 60
... touch the circum- ference will determine the two points which , being joined , will divide the cir- cumference into the concave and convex parts . PROP . VIII . THEOREM . If from any point without a circle , straight lines be drawn to ...
... touch the circum- ference will determine the two points which , being joined , will divide the cir- cumference into the concave and convex parts . PROP . VIII . THEOREM . If from any point without a circle , straight lines be drawn to ...
Página 62
... touch another internally in any point , the straight line which joins their centres being produced passes through that point . Let the circle A D E touch the circle A B C internally in the point A. The straight line which joins their ...
... touch another internally in any point , the straight line which joins their centres being produced passes through that point . Let the circle A D E touch the circle A B C internally in the point A. The straight line which joins their ...
Página 63
... touch another internally in any point , that point and the centres of the two circles are in the same straight line . This will form an exercise for the student . PROP . XII . THEOREM . If two circles touch each other externally in any ...
... touch another internally in any point , that point and the centres of the two circles are in the same straight line . This will form an exercise for the student . PROP . XII . THEOREM . If two circles touch each other externally in any ...
Página 64
... touch another A B C , internally , in more points than one . G Again , let the circle A CK touch the circle ABC externally in the point A. A CK cannot touch A B C in any other point . For , if it be possible let ACK touch A B C in ...
... touch another A B C , internally , in more points than one . G Again , let the circle A CK touch the circle ABC externally in the point A. A CK cannot touch A B C in any other point . For , if it be possible let ACK touch A B C in ...
Otras ediciones - Ver todas
The Elements of geometry; or, The first six books, with the eleventh and ... Euclides Vista completa - 1881 |
The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Sin vista previa disponible - 2016 |
Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle DEF angle EDF base BC bisected centre circle ABC circumference cone cylinder described diagonal diameter draw duplicate ratio equal angles equal Ax equal Const equiangular equimultiples Euclid ex æquali Exercise exterior angle fore given straight line gnomon homologous sides inscribed join less meet multiple opposite angle parallelogram parallelogram AC parallelopiped pentagon perpendicular polygon prism produced proposition Q. E. D. PROP reciprocally proportional rectangle contained rectilineal figure remaining angle right angles segment similar triangles solid angle sphere squares of AC straight line drawn straight lines A B THEOREM third three plane angles three straight lines triangle ABC triangle DEF triplicate ratio twice the rectangle vertex Wherefore whole angle
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.
Página 34 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Página 2 - 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 122 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Página 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Página 135 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Página 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Página 147 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
Página 37 - 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...