Elements of GeometryHilliard and Metcalf, 1825 - 224 sider |
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Side v
... It is upon this principle , considered at the same time as a definition and an axiom , that I have endeavoured to established the entire edifice of the elements . It is necessary to the understanding of this work that.
... It is upon this principle , considered at the same time as a definition and an axiom , that I have endeavoured to established the entire edifice of the elements . It is necessary to the understanding of this work that.
Side xiv
... entire or frac- tional , commensurable or incommensurable , and the proportion among the lines A , B , C , D , becomes a proportion in numbers . Hence the product of two lines A and D , which is called also their rectangle , is nothing ...
... entire or frac- tional , commensurable or incommensurable , and the proportion among the lines A , B , C , D , becomes a proportion in numbers . Hence the product of two lines A and D , which is called also their rectangle , is nothing ...
Side 28
... entire arc HMK = HPK , and it is moreover evident , that each of these arcs is a semicircumfer- ence . Fig . 57 , 58 . THEOREM . 113. If the circumferences of two circles cut each other in two points , the line which passes through ...
... entire arc HMK = HPK , and it is moreover evident , that each of these arcs is a semicircumfer- ence . Fig . 57 , 58 . THEOREM . 113. If the circumferences of two circles cut each other in two points , the line which passes through ...
Side 30
... entire arc AB will be to the entire arc DE , as 7 to 4 . Now it is evident , that the same reasoning might be used , what- ever numbers were substituted in the place of 7 and 4 ; there- fore , if the ratio of the angles ACB , DCE , can ...
... entire arc AB will be to the entire arc DE , as 7 to 4 . Now it is evident , that the same reasoning might be used , what- ever numbers were substituted in the place of 7 and 4 ; there- fore , if the ratio of the angles ACB , DCE , can ...
Side 31
Adrien Marie Legendre. entire numbers , the arcs AB , DE , will be to each other , as the angles ACB , DCE . 121. Scholium . Reciprocally , if the arcs AB , DE , are to each other , as two entire numbers , the angles ACB , DCE , will be ...
Adrien Marie Legendre. entire numbers , the arcs AB , DE , will be to each other , as the angles ACB , DCE . 121. Scholium . Reciprocally , if the arcs AB , DE , are to each other , as two entire numbers , the angles ACB , DCE , will be ...
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Vanlige uttrykk og setninger
ABC fig adjacent angles altitude angle ACB angle BAD angles equal base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle intersection isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence
Populære avsnitt
Side 65 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Side 21 - 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.
Side 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...
Side 63 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Side 22 - CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Side 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...
Side 80 - 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.
Side 164 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Side 24 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Side 153 - XVII.) ; hence two similar pyramids are to each other as the cubes of their homologous sides.