Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce Morton] 1830. Elements of trigonometry, by W. Hopkins. 1833. Elements of spherical trigonometry, by A. De Morgan. A treatise on algebraical geometry, by S.W. Waud. 1835Baldwin & Craddock, 1835 |
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Seite 79
... touch a circle , when it meets the circumference in any point , but being produced does not cut it in that point . Such a line is frequently , for brevity's sake , called a tangent ; and the point in which it meets the circumference is ...
... touch a circle , when it meets the circumference in any point , but being produced does not cut it in that point . Such a line is frequently , for brevity's sake , called a tangent ; and the point in which it meets the circumference is ...
Seite 80
... touch the circle . T For , C A being shorter ( I. 12. Cor . 3. ) than any other line which can be drawn from C to ... touching the circle . Cor . 2. ( Euc . iii . 19. ) If a straight line touches a circle , and from the point of contact ...
... touch the circle . T For , C A being shorter ( I. 12. Cor . 3. ) than any other line which can be drawn from C to ... touching the circle . Cor . 2. ( Euc . iii . 19. ) If a straight line touches a circle , and from the point of contact ...
Seite 81
... circumference of the greater circle . Therefore , & c . Cor . ( Euc . iii . 5 and 6. ) If two cir- cles cut or touch one another , they can- not have the same centre . G PROP . 7. ( EUC . iii . 10. ) III . § 1 : ] 81 GEOMETRY .
... circumference of the greater circle . Therefore , & c . Cor . ( Euc . iii . 5 and 6. ) If two cir- cles cut or touch one another , they can- not have the same centre . G PROP . 7. ( EUC . iii . 10. ) III . § 1 : ] 81 GEOMETRY .
Seite 82
... touch one another , the distance between their centres must be equal to the sum or to the difference of their radii ; the sum if they touch externally , the difference if they touch internally . Scholium . We may remark that from the ...
... touch one another , the distance between their centres must be equal to the sum or to the difference of their radii ; the sum if they touch externally , the difference if they touch internally . Scholium . We may remark that from the ...
Seite 83
... touch one another . Let A , B be the centres of two circles , the circumferences of which meet one another in the point C , which is in the line AB , or in A B produced : and let the ra- dius of the first circle be greater than the ...
... touch one another . Let A , B be the centres of two circles , the circumferences of which meet one another in the point C , which is in the line AB , or in A B produced : and let the ra- dius of the first circle be greater than the ...
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A B C ABCD adjacent angles altitude apothem base BC bisect centre chord circum circumference circumscribed coincide common measure common section compounded cone conic section contained convex surface cylinder describe a circle diameter dihedral angle divided draw drawn edges equal angles equimultiples ference fore four magnitudes frustum given point given straight line gles harmonical harmonical mean Hence hyperbola hypotenuse inscribed join likewise locus meet parallel parallelogram parallelopiped pass pendicular pentagon perimeter perpendicular plane prism Prob produced PROP proposition pyramid quadrilateral radii radius rallel rectangle rectilineal figure regular polygon respectively right angles Scholium scribed segment sides A B similar solid angles sphere spherical angle square of A B straight lines A B tangent third three sides touch triangle ABC vertex vertical