The Elements of Euclid: With Select Theorems Out of Archimedes |
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Page 166
... conical Sur- face , and the Body which is contain'd under this Sur- face , and the Circle ( CL ) is call'd a Cone . The Vertex of the Cone is ( A ) . The Circle ( CL ) is the Bafe of the Cone . The right Line ( AB ) drawn from the ...
... conical Sur- face , and the Body which is contain'd under this Sur- face , and the Circle ( CL ) is call'd a Cone . The Vertex of the Cone is ( A ) . The Circle ( CL ) is the Bafe of the Cone . The right Line ( AB ) drawn from the ...
Page 177
... conical Bodies whatsoever . PROP . XII . Theorem . HE Proportion of like Cones ( BAF and Fig . 20 , 21 QZR ) is triplicate to the Proportion of the Diameters ( BF and QR ) which are in the Bafes The fame Thing is to be faid of like ...
... conical Bodies whatsoever . PROP . XII . Theorem . HE Proportion of like Cones ( BAF and Fig . 20 , 21 QZR ) is triplicate to the Proportion of the Diameters ( BF and QR ) which are in the Bafes The fame Thing is to be faid of like ...
Page 206
... conical Surface . Corollaries . Fig . 9 , S. 1.THE Superficies of a right Cone is equal to a Tri- angle comprehended under the Side of the Cone ( BC ) and the Circumference of the Base ( CG ) . I Let OL the Radius be a mean Proportional ...
... conical Surface . Corollaries . Fig . 9 , S. 1.THE Superficies of a right Cone is equal to a Tri- angle comprehended under the Side of the Cone ( BC ) and the Circumference of the Base ( CG ) . I Let OL the Radius be a mean Proportional ...
Page 207
... Conical Superficies ( by the 13th of this ) BCD . Q. E. D. From this Corollary it appears that conical Surfaces have the fame Properties with Triangles . And fo it follows , 1. 12 . That the conical Superficies ( B AF , QXR ) ha- Fig ...
... Conical Superficies ( by the 13th of this ) BCD . Q. E. D. From this Corollary it appears that conical Surfaces have the fame Properties with Triangles . And fo it follows , 1. 12 . That the conical Superficies ( B AF , QXR ) ha- Fig ...
Page 208
... conical Superficies CBD . But the Proportion of this to A CG the Bafe of the Cone is ( by 2. l . 12. ) duplicate to the Proportion of OL to AC ; and confequently is the same with the Proportion of BC to AC . Therefore the Pro- portion ...
... conical Superficies CBD . But the Proportion of this to A CG the Bafe of the Cone is ( by 2. l . 12. ) duplicate to the Proportion of OL to AC ; and confequently is the same with the Proportion of BC to AC . Therefore the Pro- portion ...
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The Elements of Euclid: With Select Theorems Out of Archimedes Archimedes,André Tacquet,Euclid No preview available - 2015 |
Common terms and phrases
alfo alfo equal alſo Altitude Arch Archimedes Axis Bafe Baſe becauſe betwixt themſelves bifected Centre Circum circumfcrib'd Circumference confequently Conftruction conical Superficies conical Surfaces contain'd Coroll Corollary Cylinder defcrib'd defcribe demonftrated Diameter double drawn thro equal Angles equilateral Cone equilateral Triangle Euclid faid fame manner fcrib'd fecond felf fhall be equal fhew fhew'd Figure firft firſt folid Angle fome fore foregoing four right ftand fuppos'd given right Line greater hath Height Hypothefis infcrib'd infcribed Interfections leffer lefs likewife Line BC manifeft Mathematicks mean Proportional betwixt Meaſure Number oppofite pafs thro parallel Parallelepiped Parallelogram Pentagon perpendicular Plane Point Polygon Prifm Priſms Proclus produc'd PROP Propofition Pyramids Radius Rectangle right Angle right Line Scholium Segment Semidiameter Solid Sphere Square thefe Theorem theſe Thing thofe unto whatſoever whofe whole Superficies
Popular passages
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Page 211 - Side next to the Diameter : and let the right Lines BH, CG, DF, join the Angles which are equally diftant from A. I fay that the...
Page 221 - Axis, is alfo given j it is manifeft that each of the Segments become known. Now both the foregoing, and all the reft of the Theorems which follow...