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 147
... regular polygon is a rectilinear figure which has all its angles and all its sides equal to one another . Remark II . A rectilinear figure is said to be inscribed in a circle , when the vertices of all the angles of that figure are at ...
... regular polygon is a rectilinear figure which has all its angles and all its sides equal to one another . Remark II . A rectilinear figure is said to be inscribed in a circle , when the vertices of all the angles of that figure are at ...
Σελίδα 148
... regular polygon . Q. How can you prove this ? A. The circumference of the circle being divided into equal parts , it follows that the arcs AB , BC , CD , & c . and consequently also the chords AB , BC , CD , & c . which form the sides ...
... regular polygon . Q. How can you prove this ? A. The circumference of the circle being divided into equal parts , it follows that the arcs AB , BC , CD , & c . and consequently also the chords AB , BC , CD , & c . which form the sides ...
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
... regular 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 ...
... regular 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 ...
Σελίδα 152
... regular polygon , similar to the one inscrib- ed in the circle . QUERY XIX . It has been proved ( Query 16 , Sect . IV , ) that a regular pol- ygon , of any number of sides , may be inscribed in a circle , by dividing the circumference ...
... regular polygon , similar to the one inscrib- ed in the circle . QUERY XIX . It has been proved ( Query 16 , Sect . IV , ) that a regular pol- ygon , of any number of sides , may be inscribed in a circle , by dividing the circumference ...
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...