A Course of Mathematics: In Two Volumes. For the Use of the Royal Military Academy, Volume 1Gilberte and Rivington, 1841 - Mathematics |
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Page 340
... intersection . These points , must , therefore , coincide . Cor . 2. If from any point E ' in one side of a triangle lines be drawn to cut the other two , as E'GH , E'FD , and so on ; and lines be drawn from these points to the angles ...
... intersection . These points , must , therefore , coincide . Cor . 2. If from any point E ' in one side of a triangle lines be drawn to cut the other two , as E'GH , E'FD , and so on ; and lines be drawn from these points to the angles ...
Page 341
... intersection . First . LET AC : CB :: AD : DB , and the lines be drawn from A , B , C , D , to meet at F : then , if a line MKL be drawn parallel to AF , one of the extreme lines of the fasceau , it will be bisected in K. F H 3C D M K I ...
... intersection . First . LET AC : CB :: AD : DB , and the lines be drawn from A , B , C , D , to meet at F : then , if a line MKL be drawn parallel to AF , one of the extreme lines of the fasceau , it will be bisected in K. F H 3C D M K I ...
Page 342
... intersection of the tangents which cuts the circle will be harmonically divided at its intersection with the circle and its chord . LET the tangents DE , DF , drawn from D , touch the circle A in E and F , and let EF be joined : then ...
... intersection of the tangents which cuts the circle will be harmonically divided at its intersection with the circle and its chord . LET the tangents DE , DF , drawn from D , touch the circle A in E and F , and let EF be joined : then ...
Page 343
... intersection diameters be drawn ; the extremities of these diameters and the other point of intersection shall be in the same straight line . 3. If a line touching two circles cut another line joining their centres , the segments of the ...
... intersection diameters be drawn ; the extremities of these diameters and the other point of intersection shall be in the same straight line . 3. If a line touching two circles cut another line joining their centres , the segments of the ...
Page 345
... intersect the first chord at equal distances from the middle point . 47. If in a right - angled triangle a ... intersections , two tangents be drawn , one to each circle , they shall be equal to each other . 54. To cut off from a given ...
... intersect the first chord at equal distances from the middle point . 47. If in a right - angled triangle a ... intersections , two tangents be drawn , one to each circle , they shall be equal to each other . 54. To cut off from a given ...
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Common terms and phrases
ABCD algebraic altitude arithmetical arithmetical progression base bisect breadth centre chord circle circumference coefficients common cone cosec cube root decimal denominator denoted diagonal diameter difference dihedral angle distance divided divisor draw drawn equal equation equiangular EXAMPLES expression figure fraction frustum geometrical given line greater hence inscribed integer intersection join length less lineation logarithms mantissa measure meeting method multiplied parallel parallel ruler parallelogram perpendicular plane polygon prism PROBLEM proportional quantity quotient radii radius ratio rectangle Reduce right angles rule Scholium segment sides sine solid angle solution square root straight line subtraction tangent THEOREM third trapezium triangle ABC u₁ vulgar fraction Whence