Elements of Geometry Upon the Inductive Method: To which is Added an Introduction to Descriptive GeometryHilliard and Brown, 1829 - 172 σελίδες |
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Σελίδα 35
... chord and the arc is called a segment of the circle . 106. If the two radii DO , EO , the chord DE and the arc DGE , be made to revolve together about the centre O , of the circle , the points D and E will be continually in the ...
... chord and the arc is called a segment of the circle . 106. If the two radii DO , EO , the chord DE and the arc DGE , be made to revolve together about the centre O , of the circle , the points D and E will be continually in the ...
Σελίδα 36
... chord . By increasing the side DE of the triangle , we increase the angle O , and the arc which measures this angle ; therefore- The greater chord subtends the greater arc . 108. We said that the chord increases as the arc is in ...
... chord . By increasing the side DE of the triangle , we increase the angle O , and the arc which measures this angle ; therefore- The greater chord subtends the greater arc . 108. We said that the chord increases as the arc is in ...
Σελίδα 37
... chord , bisects the arc , and passes through the centre of the circle . 110. This enables us to find the centre of a circle to which any arc belongs ( fig . 53 ) . We have only to as- Fig . 53 . sume two chords , AD , DB , in the arc ...
... chord , bisects the arc , and passes through the centre of the circle . 110. This enables us to find the centre of a circle to which any arc belongs ( fig . 53 ) . We have only to as- Fig . 53 . sume two chords , AD , DB , in the arc ...
Σελίδα 38
... chord , the arc which it subtends will be bisected by this radius ( 109 ) at the point of contact . So if another parallel se- cant OP be drawn , the arc which this cuts off will also be bisected by the same radius ; so that we shall ...
... chord , the arc which it subtends will be bisected by this radius ( 109 ) at the point of contact . So if another parallel se- cant OP be drawn , the arc which this cuts off will also be bisected by the same radius ; so that we shall ...
Σελίδα 40
... chord and tangent ; for if AC be made to re- volve about the point C till it come into the position A / C as the angle ACB increases , the arc AB increases , half of it still measuring the angle ; and this reasoning holds till AC come ...
... chord and tangent ; for if AC be made to re- volve about the point C till it come into the position A / C as the angle ACB increases , the arc AB increases , half of it still measuring the angle ; and this reasoning holds till AC come ...
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Elements of Geometry Upon the Inductive Method James Hayward Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Elements of Geometry Upon the Inductive Method James Hayward Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD allel axis base bisect body called centre chord circumference co-ordinate planes conical surface construct contained cutting plane cylinder cylindrical surface Descriptive Geometry determine diagonals diameter dicular diedral distance draw equivalent exterior angles faces figure four right-angles generatrix Geometry give given line ground line height homologous horizontal plane horizontal projection horizontal trace hypothenuse inclination inscribed polygon intersection isosceles triangle line parallel lunary surface magnitude meet multiplied number of sides opposite parallel lines parallelogram parallelopiped perpen perpendicular perspective plane angles plane of projection plane passing polyedral angle polyedrons PROBLEM projecting planes proposed plane proposed point pyramid radii ratio rectangle rectilinear regular polygons revolve right-angled triangle right-line similar triangles sphere square straight line summit Suppose surface of revolution tangent tetraedron tion triangle ABC triangular prism triedral angle vertex vertical plane vertical projection volume
Δημοφιλή αποσπάσματα
Σελίδα ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Σελίδα ii - An act supplementary to an act, entitled, * An act for the encouragement of learning, by securing the copies of maps, charts, and books to the authors and proprietors of such copies, during the times therein mentioned,* and extending the benefits thereof to the arts of designing, engraving, and etching historical and other prints.
Σελίδα 13 - FGH, have a side and the two adjacent angles of the one equal to a side and the two adjacent angles of the other, each to each ; therefore these triangles are equal (Prop.
Σελίδα 65 - 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 61 - The square described upon the hypothenuse of a rightangled triangle is equivalent to the sum of the squares described upon the other two sides.
Σελίδα 12 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 63 - Prove that in any triangle the square on the side opposite an acute angle is equivalent to the sum of the squares of the other two sides diminished by twice the product of one of these sides and the projection of the other upon that side.
Σελίδα 24 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Σελίδα 62 - The rectangle contained by the sum and difference of two lines, is equivalent to the difference of the squares of those lines.
Σελίδα ii - States entitled an act for the encouragement of learning hy securing the copies of maps, charts and books to the author., and proprietors of such copies during the times therein mentioned, and also to an act entitled an act supplementary to an act, entitled an act for the encouragement of learning by securing the copies of maps, charts and books to the authors and proprietors of such copies during the times therein mentioned and extending the benefits thereof to the arts of designing, engraving and...