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 113
... polygon ABCDEF , or , in general , of any other rectilinear figure ? Ans . By dividing it by means of diagonals , ( as in F E the figure before us ) or by any other means in- to triangles . The area of each of these trian- gles is then ...
... polygon ABCDEF , or , in general , of any other rectilinear figure ? Ans . By dividing it by means of diagonals , ( as in F E the figure before us ) or by any other means in- to triangles . The area of each of these trian- gles is then ...
Σελίδα 126
... polygon ABCDEF the diagonals AC , AD , AE , and in the polygon abcdef , the corresponding diagonals a c , a d , ae , the triangle ABC , will be similar to the triangle abc , the triangle ACD , similar to the triangle a cd , the triangle ...
... polygon ABCDEF the diagonals AC , AD , AE , and in the polygon abcdef , the corresponding diagonals a c , a d , ae , the triangle ABC , will be similar to the triangle abc , the triangle ACD , similar to the triangle a cd , the triangle ...
Σελίδα 148
... ABCDEF , which will be inscribed in the circle ? A. The figure thus inscribed in the circle is a regular polygon . Q. How can you prove this ? A. The circumference of the circle being divided ... ABCDEF is a regular polygon . 148 GEOMETRY .
... ABCDEF , which will be inscribed in the circle ? A. The figure thus inscribed in the circle is a regular polygon . Q. How can you prove this ? A. The circumference of the circle being divided ... ABCDEF is a regular polygon . 148 GEOMETRY .
Σελίδα 149
Francis Joseph Grund. therefore the inscribed figure ABCDEF is a regular polygon . Q. If in this manner you divide the circumference of a circle into 3 , 4 , 5 , 6 , & c . equal parts , what will be the magnitude of each of the arcs AB ...
Francis Joseph Grund. therefore the inscribed figure ABCDEF is a regular polygon . Q. If in this manner you divide the circumference of a circle into 3 , 4 , 5 , 6 , & c . equal parts , what will be the magnitude of each of the arcs AB ...
Σελίδα 151
... polygon , of the same number of sides as the inscribed polygon ABCDEF . Q. How do you prove this ? A. The chords AB , BC , CD , & c . are perpen- dicular to the same radii , to which the tangents MN , NP , PQ , & c . are perpendicular ...
... polygon , of the same number of sides as the inscribed polygon ABCDEF . Q. How do you prove this ? A. The chords AB , BC , CD , & c . are perpen- dicular to the same radii , to which the tangents MN , NP , PQ , & c . are perpendicular ...
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...