A Course of Mathematics: In Two Volumes : for the Use of Academies, as Well as Private Tuition, Volume 1Samuel Campbell, Evert Duyckinck, T. & J. Swords, 1816 - Mathematics |
From inside the book
Results 1-5 of 32
Page 317
... Circumscribing Circle . LET CD be the perpendicular , and oE the diameter of the circle about the triangle ABC ; then the rectangle CA. CB is the rectangle CD . CE = For , join BE : then in the two triangles ACD , ECB , the angles A and ...
... Circumscribing Circle . LET CD be the perpendicular , and oE the diameter of the circle about the triangle ABC ; then the rectangle CA. CB is the rectangle CD . CE = For , join BE : then in the two triangles ACD , ECB , the angles A and ...
Page 351
... Circumscribing Cylinder . LET ABCD be a cylinder , circum- scribing the sphere EFGH ; then will the sphere EFGH be two - thirds of the cylinder ABCD . AFB MX 0 E D For , let the plane AC be a section of the sphere and cylinder through ...
... Circumscribing Cylinder . LET ABCD be a cylinder , circum- scribing the sphere EFGH ; then will the sphere EFGH be two - thirds of the cylinder ABCD . AFB MX 0 E D For , let the plane AC be a section of the sphere and cylinder through ...
Page 352
... circumscribing cylinders . Corol . 3. From the foregoing demonstration it also ap- pears , that the spherical zone or frustrum EGNP , is equal to the difference between the cylinder EGLO and the cone IMQ , all of the same common height ...
... circumscribing cylinders . Corol . 3. From the foregoing demonstration it also ap- pears , that the spherical zone or frustrum EGNP , is equal to the difference between the cylinder EGLO and the cone IMQ , all of the same common height ...
Page 365
... circumscribing circle , or to the chord of one - sixth part of the circumference . PROBLEM XXXI . K H To describe a ... circumscribed figure is both equilateral and equiangular , which was to be shown . Corol . Corol . The inscribed ...
... circumscribing circle , or to the chord of one - sixth part of the circumference . PROBLEM XXXI . K H To describe a ... circumscribed figure is both equilateral and equiangular , which was to be shown . Corol . Corol . The inscribed ...
Page 366
... circle described with the centre o and radius oa , will pass through all the other angular points , B , C , D , & c , and will circumscribe the polygon . PROBLEM PROBLEM XXXIV . To make a Square Equal to the 366 GEOMETRY .
... circle described with the centre o and radius oa , will pass through all the other angular points , B , C , D , & c , and will circumscribe the polygon . PROBLEM PROBLEM XXXIV . To make a Square Equal to the 366 GEOMETRY .
Contents
223 | |
230 | |
249 | |
257 | |
266 | |
275 | |
281 | |
319 | |
68 | |
76 | |
77 | |
92 | |
111 | |
119 | |
127 | |
135 | |
150 | |
159 | |
167 | |
175 | |
181 | |
188 | |
199 | |
206 | |
213 | |
336 | |
353 | |
369 | |
377 | |
379 | |
398 | |
419 | |
429 | |
457 | |
466 | |
473 | |
491 | |
514 | |
532 | |
558 | |
571 | |
Other editions - View all
Common terms and phrases
ABCD abscisses ac² altitude arithmetical arithmetical progression axis base bisected CA² CD² centre chord circle circumference common compound cone consequently cube root cubic equation cylinder decimal denominator denotes diameter difference distance divide dividend divisor draw equal angles equal th equation equiangular equilateral EXAMPLES feet figure fraction frustum geometrical progression given number gives greater Hence improper fraction inches infinite series inscribed length Let ABC logarithm manner measured by half multiply ordinates parallel parallelogram perpendicular plane polygon prism PROBLEM proportional Q. E. D. Corol Q. E. D. THEOREM quantity QUEST quotient radii radius ratio rectangle Reduce right angles right line right-angled triangle rule side AC sine square root subtract surd tangent theor theref transposing triangle ABC VULGAR FRACTIONS whole number yards
Popular passages
Page 6 - Los números cardinales 0: zero 1: one 2: two 3: three 4: four 5: five 6: six 7: seven 8: eight 9: nine 10: ten 11: eleven 12: twelve 13: thirteen 14: fourteen 15: fifteen 16: sixteen 17: seventeen 18: eighteen 19: nineteen 20: twenty...
Page 285 - AB>AC-BC: that is, the difference of any two sides of a triangle is less than the third side.
Page 438 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 187 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.
Page 202 - Subtract its power from that term, and bring down the second term for a dividend. 3. Involve the root, last found, to the next lowest -power, and multiply it by the index of the given power for a divisor.
Page 290 - A perpendicular is the shortest line that can be drawn from a given point to a given line.
Page 86 - Then say, by the rule of three, as the sum of the given number and double the assumed cube is to the sum of the assumed cube and double the given number, so is the root of the assumed cube to the root required, nearly ; Or as the first sum is to the difference of the given and assumed...
Page 398 - Two ships of war, intending to cannonade a fort, are, by the shallowness of the water, kept so far from it, that they suspect their guns cannot reach it with effect. In order, therefore, to measure the distance, they separate from each other a quarter of a mile, or 440 yards ; then each ship observes and measures the angle which the other ship and the fort subtend, which angles are 83° 45
Page 355 - B draw chords BA, BC, to the two other points, and bisect these chords perpendicularly by lines meeting in O, which will be the centre. Then from the centre O, at the distance of any one of the points, as ( ) A, describe a circle, and it will pass through the two other points B, C, as required.
Page 56 - To reduce an improper fraction to a whole, or mixed number. Divide the numerator by the denominator, and the quotient will be the whole, or mixed number required.