Elements of Geometry and Trigonometry |
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Page 30
If from the vertex of any one angle A , diagonals B. AC , AD , AE , AF , be drawn to the vertices of all the opposite angles , it is plain that the poly- gon will be divided into five triangles , if it has seven sides ; into six ...
If from the vertex of any one angle A , diagonals B. AC , AD , AE , AF , be drawn to the vertices of all the opposite angles , it is plain that the poly- gon will be divided into five triangles , if it has seven sides ; into six ...
Page 33
D C B For , draw the diagonal DB , dividing the quadrilateral into two triangles . Then , since AB is parallel to DC , the alternate angles ABD , BDC , are equal ( Prop . XX . Cor . 2. ) ; moreover , the side DB is common , and the side ...
D C B For , draw the diagonal DB , dividing the quadrilateral into two triangles . Then , since AB is parallel to DC , the alternate angles ABD , BDC , are equal ( Prop . XX . Cor . 2. ) ; moreover , the side DB is common , and the side ...
Page 34
Ratio is the quotient arising from dividing one quantity by another quantity of the same kind . ... Thus , of two magnitudes , one of them may be considered to be divided into some number of equal parts , each of the same kind as the ...
Ratio is the quotient arising from dividing one quantity by another quantity of the same kind . ... Thus , of two magnitudes , one of them may be considered to be divided into some number of equal parts , each of the same kind as the ...
Page 35
Two quantities A and B are said to be reciprocally pro- portional , or , invasely proportional , when one of them is pro- portional to unity divided by the other , in which case their ...
Two quantities A and B are said to be reciprocally pro- portional , or , invasely proportional , when one of them is pro- portional to unity divided by the other , in which case their ...
Page 52
M The seven partial angles ACm , mCn , nCp , & c . , into which ACB is divided , being each equal to any of the four partial angles into which DCE is divided ; each of the partial arcs Am , mn , np , & c . , will be equal to each of the ...
M The seven partial angles ACm , mCn , nCp , & c . , into which ACB is divided , being each equal to any of the four partial angles into which DCE is divided ; each of the partial arcs Am , mn , np , & c . , will be equal to each of the ...
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ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole