Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce Morton] 1830. Elements of trigonometry, by W. Hopkins. 1833. Elements of spherical trigonometry, by A. De Morgan. A treatise on algebraical geometry, by S.W. Waud. 1835Baldwin & Craddock, 1835 |
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Σελίδα 32
... common measure , are said to be incommen- surable . Magnitudes A , B , which have one common measure M , have also many others , indeed , an unlimited number of common measures , for ( as will be shown in Prop . 1. ) every magnitude ...
... common measure , are said to be incommen- surable . Magnitudes A , B , which have one common measure M , have also many others , indeed , an unlimited number of common measures , for ( as will be shown in Prop . 1. ) every magnitude ...
Σελίδα 33
... common numerical ratio : and , in every case , if two magnitudes , and other two , have a common numerical ratio , the four magnitudes are , accord- ing to this definition , proportionals . It is evident from the observations on def . 6 ...
... common numerical ratio : and , in every case , if two magnitudes , and other two , have a common numerical ratio , the four magnitudes are , accord- ing to this definition , proportionals . It is evident from the observations on def . 6 ...
Σελίδα 34
... common factor , the same ratio may be expressed by any terms , as 5 : 6 , which are like parts of the given terms . For , if M be the common measure which is contained in A 10 × 5 times , and in B 10x 6 times , it is evident that 10 M ...
... common factor , the same ratio may be expressed by any terms , as 5 : 6 , which are like parts of the given terms . For , if M be the common measure which is contained in A 10 × 5 times , and in B 10x 6 times , it is evident that 10 M ...
Σελίδα 35
... common measure of the two magnitudes shall measure the re- mainder , and any common measure of the remainder and the lesser magnitude , shall measure the greater also . Let B be contained in A twice with a remainder R , and let M be A ...
... common measure of the two magnitudes shall measure the re- mainder , and any common measure of the remainder and the lesser magnitude , shall measure the greater also . Let B be contained in A twice with a remainder R , and let M be A ...
Σελίδα 36
... common measure is contained in each ( see def . 6. ) . Scholium . It may be observed that the foregoing process includes the arithmetical rule for finding the greatest common factor of two numbers : which is to divide the greater number ...
... common measure is contained in each ( see def . 6. ) . Scholium . It may be observed that the foregoing process includes the arithmetical rule for finding the greatest common factor of two numbers : which is to divide the greater number ...
Άλλες εκδόσεις - Προβολή όλων
Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ... Πλήρης προβολή - 1835 |
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C ABCD adjacent angles altitude apothem base BC bisect centre chord circum circumference circumscribed coincide common measure common section compounded cone conic section contained convex surface cylinder describe a circle diameter dihedral angle divided draw drawn edges equal angles equimultiples ference fore four magnitudes frustum given point given straight line gles harmonical harmonical mean Hence hyperbola hypotenuse inscribed join likewise locus meet parallel parallelogram parallelopiped pass pendicular pentagon perimeter perpendicular plane prism Prob produced PROP proposition pyramid quadrilateral radii radius rallel rectangle rectilineal figure regular polygon respectively right angles Scholium scribed segment sides A B similar solid angles sphere spherical angle square of A B straight lines A B tangent third three sides touch triangle ABC vertex vertical