First lessons in Plane Geometry. Together with an application of them to the solution of problems, etcCarter and Hendee, 1830 - 12 σελίδες |
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Σελίδα 67
Francis Joseph Grund. between the two terms , AB , ab , of a ratio , is obvious ; for a ratio points out how many times one term ( the side a b ) is contained in another , ( the side AB ) . The first and fourth term of a proportion , to ...
Francis Joseph Grund. between the two terms , AB , ab , of a ratio , is obvious ; for a ratio points out how many times one term ( the side a b ) is contained in another , ( the side AB ) . The first and fourth term of a proportion , to ...
Σελίδα 70
... fourth a ratio common with the third , and so on , the sum of all the first terms of these proportions will bear the ... term ; and consequently each of the third terms , bc , ab , is half of its corresponding fourth term ; therefore ...
... fourth a ratio common with the third , and so on , the sum of all the first terms of these proportions will bear the ... term ; and consequently each of the third terms , bc , ab , is half of its corresponding fourth term ; therefore ...
Σελίδα 71
... terms are exactly one half of the second and fourth terms , yet it is easy to perceive , that the same course * The lines over abac , AB + AC , & c . , mark that abac , AB + AC , & c . , are but single lines composed of the two parts ...
... terms are exactly one half of the second and fourth terms , yet it is easy to perceive , that the same course * The lines over abac , AB + AC , & c . , mark that abac , AB + AC , & c . , are but single lines composed of the two parts ...
Σελίδα 72
... fourth , or one fifth , & c . , of the corresponding second terms , the sum of the first terms would also be one ... term ; and in the same way would each of the three lines , a c , bc , ab , be one half of its cor- responding part in the ...
... fourth , or one fifth , & c . , of the corresponding second terms , the sum of the first terms would also be one ... term ; and in the same way would each of the three lines , a c , bc , ab , be one half of its cor- responding part in the ...
Σελίδα 73
... fourth terms . And in like manner could this principle be extended to four , five , six , and more proportions . 5th . Another principle , which it is important to recollect , is , that by adding the second term ... term , and the fourth term ...
... fourth terms . And in like manner could this principle be extended to four , five , six , and more proportions . 5th . Another principle , which it is important to recollect , is , that by adding the second term ... term , and the fourth term ...
Άλλες εκδόσεις - Προβολή όλων
First Lessons in Plane Geometry: Together with an Application of Them to the ... Francis Joseph Grund Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2009 |
First Lessons in Plane Geometry: Together with an Application of Them to the ... Francis Joseph Grund Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2009 |
Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles angle ABC angle ACB angle opposite angle x basis and height bisected called centre chord circum circumference circumscribed circle consequently construct the triangle DEMON diagonal diameter draw the lines equal angles exterior angle figure ABCDEF found by multiplying fourth term geometrical figures geometrical proportion given angle given circle given straight line given triangle hypothenuse isosceles triangle line AB line AC line CD line MN LUDOLPH VAN CEULEN mean proportional number of sides parallel lines parallelogram perpendicular points of division PROBLEM prove quadrilateral Query 11 radii radius ratio rectilinear figure regular polygon ABCDEF remaining sides Remark right angles right-angular triangle Sect semicircle side AB side AC similar triangles smaller SOLUTION square feet square inches square seconds tangent third line three angles three sides trapezoid trian triangle ABC triangle are equal vertex zoid
Δημοφιλή αποσπάσματα
Σελίδα 195 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.
Σελίδα 94 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...
Σελίδα 211 - HDG, the corresponding sides are proportional (page 70, 4thly) ; therefore we have the proportion ED : DG =AD : HD (II.) This last proportion has the first ratio common with the first proportion ; consequently the two remaining ratios are in a geometrical proportion (Theory of Prop., Prin. 3d) ; that is, we have AD : HD = DG: BD; and as, in...
Σελίδα 173 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Σελίδα 176 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Σελίδα 175 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Σελίδα 129 - Now, since the areas of similar polygons are to each other as the squares of their homologous sides...