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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Seite 159
... picture or plane of delinea- tion . The respective positions of the eye , the picture , and the object , must be determined , in order that the image may be determined . The knowledge of the true form and dimensions of * This supposes ...
... picture or plane of delinea- tion . The respective positions of the eye , the picture , and the object , must be determined , in order that the image may be determined . The knowledge of the true form and dimensions of * This supposes ...
Seite 160
... picture , situated in any manner whatever , the appearance or the perspective of a point given in space . Take the vertical projection of the proposed point , on a plane perpendicular to the common intersection of the plane of the picture ...
... picture , situated in any manner whatever , the appearance or the perspective of a point given in space . Take the vertical projection of the proposed point , on a plane perpendicular to the common intersection of the plane of the picture ...
Seite 161
... picture itself for the co - ordinate vertical plane . The eye , being supposed behind the plane of the picture , ( fig . 42 ) has its horizontal projection in O ' ; that Fig . 42 . of the point in question is in P ' , and p is the ...
... picture itself for the co - ordinate vertical plane . The eye , being supposed behind the plane of the picture , ( fig . 42 ) has its horizontal projection in O ' ; that Fig . 42 . of the point in question is in P ' , and p is the ...
Seite 163
... picture , determines the perspective of this straight line ; but the line OO ' ( fig . 43 ) being parallel to the proposed line and Fig . 43 . passing through the eye which we suppose in O , is situ- ated necessarily in this plane ...
... picture , determines the perspective of this straight line ; but the line OO ' ( fig . 43 ) being parallel to the proposed line and Fig . 43 . passing through the eye which we suppose in O , is situ- ated necessarily in this plane ...
Seite 164
... picture , must meet in this point . We project the proposed point P upon the plane of the picture , which we suppose to be vertical ; the point P " where this projection falls , will be that in which the per- pendicular drawn from the ...
... picture , must meet in this point . We project the proposed point P upon the plane of the picture , which we suppose to be vertical ; the point P " where this projection falls , will be that in which the per- pendicular drawn from the ...
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Häufige Begriffe und Wortgruppen
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.