Elements of Geometry Upon the Inductive Method: To which is Added an Introduction to Descriptive GeometryHilliard and Brown, 1829 - 172 Seiten |
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... radius ? 8. A surface to which a straight line can be applied in every direction , so as to touch the surface through the whole extent of the line , is called a plane surface , or simply a plane . A surface which is neither a plane ...
... radius ? 8. A surface to which a straight line can be applied in every direction , so as to touch the surface through the whole extent of the line , is called a plane surface , or simply a plane . A surface which is neither a plane ...
Seite 7
... radius , from the vertices of the angles , as centres , will be also equal . We hence see how the magnitude of an an- gle may be designated by a circular arc . For this purpose , the ancients divided the circumfe- rence of the circle ...
... radius , from the vertices of the angles , as centres , will be also equal . We hence see how the magnitude of an an- gle may be designated by a circular arc . For this purpose , the ancients divided the circumfe- rence of the circle ...
Seite 9
... radius , describe the arc de ; then from d as a cen- tre with a radius equal to DE , describe another arc cut- ting the arc de , in the point e ; and through the points c and e , draw the line ce a , and you have the angle a cb , equal ...
... radius , describe the arc de ; then from d as a cen- tre with a radius equal to DE , describe another arc cut- ting the arc de , in the point e ; and through the points c and e , draw the line ce a , and you have the angle a cb , equal ...
Seite 11
... radius equal to the given line B , describe an arc ; and from E as a centre , with a radius equal to the other given line C , describe an arc cutting the other arc in F ; draw DF and EF , and you have the triangle required . 39. It is ...
... radius equal to the given line B , describe an arc ; and from E as a centre , with a radius equal to the other given line C , describe an arc cutting the other arc in F ; draw DF and EF , and you have the triangle required . 39. It is ...
Seite 13
... radius equal to the given hypothenuse , draw an arc cutting the perpendicular in E ; draw CE , and you have the right - angled triangle required . [ Let the learner show that no different triangle could be construct- ed with these ...
... radius equal to the given hypothenuse , draw an arc cutting the perpendicular in E ; draw CE , and you have the right - angled triangle required . [ Let the learner show that no different triangle could be construct- ed with these ...
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ABCD allel axis base body called centre chord circ circumference circumscribed co-ordinate planes common conical surface construct contained cutting plane cylinder cylindrical surface Descriptive Geometry diagonals diameter diedral distance draw equivalent exterior angles faces figure four right-angles generatrix give given line ground line height homologous horizontal plane horizontal projection horizontal trace hypothenuse inclination inscribed polygon intersection isosceles triangle lines parallel lunary surface magnitude measure meet multiplied number of sides opposite parallel lines parallelogram parallelopiped perpen perpendicular perspective plane angles plane of projection polyedral angle polyedrons prism PROBLEM projecting planes proposed plane proposition pyramid radii ratio rectangle rectilinear regular polygons right-angled triangle right-line similar triangles sphere square straight line summit Suppose surface of revolution tangent tetraedron tion triangle ABC triangular triangular prism triedral angle truth vertex vertical plane vertical projection volume
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Seite 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...
Seite xvi - 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.
Seite 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.
Seite xvii - 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.
Seite 51 - 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.
Seite 47 - The square described upon the hypothenuse of a rightangled triangle is equivalent to the sum of the squares described upon the other two sides.
Seite xi - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.
Seite 10 - 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.
Seite ii - CLERK'S OFFIcE. BE it remembered, that on the eleventh day of November, AD 1830, in the fiftyfifth year of the Independence of the United States of America, Gray & Bowen, of the said district, have deposited in this office the title of a book, the right whereof...
Seite 49 - 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.