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 49
... heights of these triangles , the radii of the inscribed cir- cles ; it follows ( 92 ) that - In regular polygons of the same number of sides , the perimeters are to each other as the radii of the circumscribed circles , and also as the ...
... heights of these triangles , the radii of the inscribed cir- cles ; it follows ( 92 ) that - In regular polygons of the same number of sides , the perimeters are to each other as the radii of the circumscribed circles , and also as the ...
Seite 53
... height of the triangle . 81 151. To compare two parallelograms ABCD , ABEF , ( fig . 81 ) whose bases are equal , and heights equal , place Fig . their bases together as in figure 82. On account of their Fig . 82 . equal heights and the ...
... height of the triangle . 81 151. To compare two parallelograms ABCD , ABEF , ( fig . 81 ) whose bases are equal , and heights equal , place Fig . their bases together as in figure 82. On account of their Fig . 82 . equal heights and the ...
Seite 54
... height . And consequently — All triangles of equal bases and equal heights , are equivalent . area . 154. We see that the triangle and parallelogram are both referred to the rectangle for the measure of their If then we can find the ...
... height . And consequently — All triangles of equal bases and equal heights , are equivalent . area . 154. We see that the triangle and parallelogram are both referred to the rectangle for the measure of their If then we can find the ...
Seite 55
... heights . 157. As a triangle is equivalent to half the rectangle of the same base and height , it follows from the last two articles , that - Two triangles , of equal heights , are to Fig . 86 . each other in the ratio of Elements of ...
... heights . 157. As a triangle is equivalent to half the rectangle of the same base and height , it follows from the last two articles , that - Two triangles , of equal heights , are to Fig . 86 . each other in the ratio of Elements of ...
Seite 56
... height , and CE X CG is the product of the base of the rectan- gle CEFG by its height . Therefore - Two rectangles are to each other as the products of their bases by their heights . 159. It is usual to estimate areas by square feet ...
... height , and CE X CG is the product of the base of the rectan- gle CEFG by its height . Therefore - Two rectangles are to each other as the products of their bases by their heights . 159. It is usual to estimate areas by square feet ...
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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.