Elements of Plane Geometry: For the Use of SchoolsLewis & Sampson, 1844 - 96 σελίδες |
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Αποτελέσματα 1 - 5 από τα 7.
Σελίδα 83
... regular polygons . PROP . I. THEOREM . Two regular polygons of the same number of sides , are similar . Let the figures in the margin be two regular polygons , having the same number of sides . The sum of all the angles in each figure ...
... regular polygons . PROP . I. THEOREM . Two regular polygons of the same number of sides , are similar . Let the figures in the margin be two regular polygons , having the same number of sides . The sum of all the angles in each figure ...
Σελίδα 84
... regular hexagon , inscribed in a circle , is equal to the radius of that circle . Let ABCDEF be a regular hexagon . Now since the arcs subtended by equal chords are equal , the three arcs AB , BC , CD , are to- gether equal to the three ...
... regular hexagon , inscribed in a circle , is equal to the radius of that circle . Let ABCDEF be a regular hexagon . Now since the arcs subtended by equal chords are equal , the three arcs AB , BC , CD , are to- gether equal to the three ...
Σελίδα 85
... regular inscribed polygon being given , to circum- scribe a similar one about the same circle . Let ABCDEF be the regular inscribed polygon . Bisect the arcs AB , BC , & c . , in the points S , R , & c . , and at these points draw GH ...
... regular inscribed polygon being given , to circum- scribe a similar one about the same circle . Let ABCDEF be the regular inscribed polygon . Bisect the arcs AB , BC , & c . , in the points S , R , & c . , and at these points draw GH ...
Σελίδα 87
... regular ; and having the same number of sides with the inscribed polygon , is similar to it ( Prop . 1 ) . PROP . V. PROBLEM . A regular circumscribed polygon being given , it is required to circumscribe the circle by another regular ...
... regular ; and having the same number of sides with the inscribed polygon , is similar to it ( Prop . 1 ) . PROP . V. PROBLEM . A regular circumscribed polygon being given , it is required to circumscribe the circle by another regular ...
Σελίδα 88
... regular circumscribed polygon , the nearer its surface approaches to that of the circle . PROP . VI . THEOREM . The area of a regular polygon is equal to its perimeter multiplied by half the line drawn from the centre of the ...
... regular circumscribed polygon , the nearer its surface approaches to that of the circle . PROP . VI . THEOREM . The area of a regular polygon is equal to its perimeter multiplied by half the line drawn from the centre of the ...
Άλλες εκδόσεις - Προβολή όλων
Elements of Plane Geometry: For the Use of Schools - Primary Source Edition Nicholas Tillinghast Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2013 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent angles allel alternate angles altitude angle ABC angles ABD angles is equal antecedent and consequent B. I. Ax base centre circle whose radius circumference circumscribed circumscribed circle Converse of Prop describe an arc diagonal diameter divide draw the line equal angles equal B. I. Prop equal chords equal Prop equal respectively equiangular equivalent feet given angle given line given point given side half hence the triangles hypotenuse included angle inscribed angle Let the triangles line drawn linear units longer than AC multiplied number of sides oblique lines parallel to CD parallelogram perimeter perpendicular PROBLEM prove radii rectangle regular polygons respectively equal right angles Prop right-angled triangle Scholium sides AC similar subtended tangent THEOREM three sides triangles ABC triangles are equal vertex
Δημοφιλή αποσπάσματα
Σελίδα 31 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.
Σελίδα 63 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Σελίδα 70 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Σελίδα 53 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 87 - 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 54 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Σελίδα 81 - 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.
Σελίδα 59 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Σελίδα 61 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.
Σελίδα 82 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.