A system of practical mathematics; being no.xvi. of a new series of school-books |
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Side 113
... meets them , the Ls ABC , BCD C e equal , but the ABC is measured by If the arc AC , ( Prop . 47 , Cor . 2 ) , and e LBCD is measured by half the arc D , .. the arc AC is the arc BD . A a r2L . B Cor . If the adjacent extremities A , B ...
... meets them , the Ls ABC , BCD C e equal , but the ABC is measured by If the arc AC , ( Prop . 47 , Cor . 2 ) , and e LBCD is measured by half the arc D , .. the arc AC is the arc BD . A a r2L . B Cor . If the adjacent extremities A , B ...
Side 114
... meet when produced in a point E , the angle AEC formed at their intersection is measured by half the difference of the intercepted arcs AC and BD . For , join BC , then the LAEC is equal to the difference of the Ls ABC and BCD , ( Prop ...
... meet when produced in a point E , the angle AEC formed at their intersection is measured by half the difference of the intercepted arcs AC and BD . For , join BC , then the LAEC is equal to the difference of the Ls ABC and BCD , ( Prop ...
Side 115
Scottish school-book assoc. Cor . If a chord CD produced , meet a tangent EF in the point E , the angle CEF is measured by half the differ- ence of the arcs CF and FD . For the GEC is the difference of the Ls GFC and FCE , ( Prop . 19 ) ...
Scottish school-book assoc. Cor . If a chord CD produced , meet a tangent EF in the point E , the angle CEF is measured by half the differ- ence of the arcs CF and FD . For the GEC is the difference of the Ls GFC and FCE , ( Prop . 19 ) ...
Side 118
... meet CE in E. Then AD is to EC , the exterior [ BAD = the in- terior LAEC , and the alternate 4s DAC , ACE , are equal ; but the BAD is the LDAC ; .. the LAEC is also the LACE ; hence the side AE is the side AC , and . AD is || to EC ...
... meet CE in E. Then AD is to EC , the exterior [ BAD = the in- terior LAEC , and the alternate 4s DAC , ACE , are equal ; but the BAD is the LDAC ; .. the LAEC is also the LACE ; hence the side AE is the side AC , and . AD is || to EC ...
Side 119
... meet , if produced , ( Prop . 17 , cor . ) ; let them meet in F , then since the ZEBA the DCB , and the LEAB = the [ DBC , ( Prop . 16 , cor . 1. ) , FD is || EB , and EF is || BD , .. also FD = EB , and EF - BD , ( Prop . 24. ) Now ...
... meet , if produced , ( Prop . 17 , cor . ) ; let them meet in F , then since the ZEBA the DCB , and the LEAB = the [ DBC , ( Prop . 16 , cor . 1. ) , FD is || EB , and EF is || BD , .. also FD = EB , and EF - BD , ( Prop . 24. ) Now ...
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A System of Practical Mathematics: Being No.XVI. of a New Series of School-Books Scottish School-Book Assoc Ingen forhåndsvisning tilgjengelig - 2016 |
Vanlige uttrykk og setninger
ABCD acres altitude annuity base bisected breadth bushels cask cent centre chord circle circumference coefficient common Cosec Cosine cubic denominator depth diagonal diameter difference distance divided divisor draw equal equation EXAMPLE EXERCISES feet figure Find the area Find the sum Find the surface fraction frustum gallons gauge given greater height hence hypotenuse inches LADC latitude least common multiple length less logarithm miles Multiply number of sides parallel Parallel Sailing parallelogram parallelopipeds perpendicular plane Plane Sailing poles polygon prism Prop proportional PROPOSITION pyramid quotient radius ratio remainder right angles RULE sailed SCHOLIUM Secant Cotang segment side AC Sine slant height solid angles specific gravity square root station straight line subtract surd surface and solidity Tang tangent THEOREM trapezium triangle ullage unknown quantities yards
Populære avsnitt
Side 122 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 113 - The first of four magnitudes is said to have the same ratio to the second, which the third has to the fourth, when any equimultiples whatsoever of the first and third being taken, and any equimultiples whatsoever of the second and fourth; if the multiple of the first be less than that of the second, the multiple of the third is also less than that of the fourth : or...
Side 77 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Side 78 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Side 82 - ... is supposed . to be divided into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds. Degrees, minutes, and seconds, are designated respectively, by the characters ° ' ". For example, ten degrees, eighteen minutes, and fourteen seconds, would be written 10° 18
Side 78 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Side 134 - To draw a straight line perpendicular to a plane, from a given point above it. Let A be the given point above the plane BH ; it is required to draw from the point A a straight line perpendicular to the plane BH.
Side 116 - ... of the base, have the same ratio which the other sides of the triangle have to one...
Side 69 - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
Side 123 - Weigh the denser body and the compound mass, separately, both in water and out of it ; then find how much each loses in water, by subtracting its weight in water from its weight in air ; and subtract the less of these remainders from the greater. Then...