Elements of Plane Geometry: For the Use of Schools |
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Page 32
... . Generally any polygon is inscribed , when the vertices of all its angles are in the circumference ; the circle is then said to circumscribe the polygon . 17. A circle is inscribed in a polygon , when 32 [ BOOK II . DEFINITIONS .
... . Generally any polygon is inscribed , when the vertices of all its angles are in the circumference ; the circle is then said to circumscribe the polygon . 17. A circle is inscribed in a polygon , when 32 [ BOOK II . DEFINITIONS .
Page 33
... circumscribe the circle . 18. Equal circles are those which are described with equal radii . PROP . I. THEOREM . Every diameter divides the circle and its circumfer- ence into two equal parts . To prove this , suppose the portion ADB ...
... circumscribe the circle . 18. Equal circles are those which are described with equal radii . PROP . I. THEOREM . Every diameter divides the circle and its circumfer- ence into two equal parts . To prove this , suppose the portion ADB ...
Page 86
... circumscribed polygon GHIKLP , which we have to prove will be similar to the inscribed one . Draw from H , the point where the tangents HG , HI , intersect , the line HO ; we shall show that it will pass through B. The arcs BRC , BSA ...
... circumscribed polygon GHIKLP , which we have to prove will be similar to the inscribed one . Draw from H , the point where the tangents HG , HI , intersect , the line HO ; we shall show that it will pass through B. The arcs BRC , BSA ...
Page 87
... circumscribed polygon being given , it is required to circumscribe the circle by another regular polygon of double the number of sides of the given one . Fig . 92 . RA B C E Circumscribe the circle with a square , and bisect the arcs AF ...
... circumscribed polygon being given , it is required to circumscribe the circle by another regular polygon of double the number of sides of the given one . Fig . 92 . RA B C E Circumscribe the circle with a square , and bisect the arcs AF ...
Page 88
... 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 circumscribed ...
... 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 circumscribed ...
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Elements of Plane Geometry: For the Use of Schools - Primary Source Edition Nicholas Tillinghast No preview available - 2013 |
Common terms and phrases
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
Popular passages
Page 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.
Page 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.
Page 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'.
Page 53 - In any proportion, the product of the means is equal to the product of the extremes.
Page 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.
Page 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.
Page 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.
Page 59 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 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.
Page 82 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.