Elements of Geometry and Trigonometry: With NotesJ. Ryan, 1828 - 316 sider |
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Side xiii
... THEOREM I. If four magnitudes are proportional , the product of the ex- tremes will be equal to that of the means ; and conversely , if two products are equal , any two factors composing the first will form the extremes of a proportion ...
... THEOREM I. If four magnitudes are proportional , the product of the ex- tremes will be equal to that of the means ; and conversely , if two products are equal , any two factors composing the first will form the extremes of a proportion ...
Side xiv
... it depends on a knowledge of the objects treated of by the ques- tion ; which objects may be geometrical , mechanical , com- mercial , or of any conceivable kind . THEOREM II . The ratio of two magnitudes is not xiv INTRODUCTION .
... it depends on a knowledge of the objects treated of by the ques- tion ; which objects may be geometrical , mechanical , com- mercial , or of any conceivable kind . THEOREM II . The ratio of two magnitudes is not xiv INTRODUCTION .
Side xv
... Theorem A : BAC ± E : B ± D ± F . And the same may be shown of any number of magnitudes having the same ratio . Cor ... Theorem , we have A + B : A - B :: C + D : C - D ; which is said to be miscendo . THEOREM III . The products of the ...
... Theorem A : BAC ± E : B ± D ± F . And the same may be shown of any number of magnitudes having the same ratio . Cor ... Theorem , we have A + B : A - B :: C + D : C - D ; which is said to be miscendo . THEOREM III . The products of the ...
Side 4
... theorem , or the solution of a problem . The common name , proposition , is applied indifferently to theorems , problems , and lemmas . A corollary is an obvious consequence deduced from one or several propositions . A scholium is a ...
... theorem , or the solution of a problem . The common name , proposition , is applied indifferently to theorems , problems , and lemmas . A corollary is an obvious consequence deduced from one or several propositions . A scholium is a ...
Side 5
... THEOREM .小 27. All right angles are equal to each other . LET the straight line CD be perpendicu- lar to AB , and GH to EF ; the angles ACD and EGH will be equal to each other . D K B H G F Take the four distances CA , CB , GE , A GF ...
... THEOREM .小 27. All right angles are equal to each other . LET the straight line CD be perpendicu- lar to AB , and GH to EF ; the angles ACD and EGH will be equal to each other . D K B H G F Take the four distances CA , CB , GE , A GF ...
Andre utgaver - Vis alle
Elements of Geometry and Trigonometry: With Notes Adrien Marie Legendre Uten tilgangsbegrensning - 1830 |
Elements of Geometry and Trigonometry, with Notes Adrien Marie Legendre Uten tilgangsbegrensning - 1832 |
Elements Of Geometry And Trigonometry From The Works Of A.m. Legendre Adrien Marie Legendre Ingen forhåndsvisning tilgjengelig - 2019 |
Vanlige uttrykk og setninger
ABCD adjacent angles altitude angle ACB angle BAD base bisect centre chord circ circle circular sector circumference circumscribed common cone construction continued fraction convex surface cosines cylinder diameter dicular draw drawn equal angles equation equivalent figure formed formulas four right angles frustum given angle given line gles greater homologous sides hypotenuse inclination inscribed intersection isosceles less Let ABC let fall likewise measure multiplied number of sides oblique lines opposite parallel parallelepipedon parallelogram pendicular perimeter perpen perpendicular plane MN polyedron prism proposition quadrilateral radii radius ratio rectangle regular polygon respectively equal right angles right-angled triangle SABC Scholium sector segment similar sine solid angle solid described sphere spherical polygons spherical triangle square straight line suppose tang tangent THEOREM third side three angles trian triangle ABC triangular prism triangular pyramids vertex vertices
Populære avsnitt
Side 257 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.
Side iii - District, has deposited in this office the title of a book, the right whereof he claims as proprietor, in the words following, to wit : " THE CHILD'S BOTANY," In conformity to the act of the Congress of the United States, 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...
Side 187 - For, if the arc AD be drawn from the vertex A to the middle point D of the base, the two triangles ABD, ACD, will have all the sides of the one respectively equal to the corresponding sides of the other...
Side 3 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Side 27 - 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 11 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.
Side 73 - If two polygons are composed of the same number of triangles, similar each to each, and similarly placed, the polygons are similar. In the two polygons ABCDE and A'B'C'D'E', let the triangles AEB, EEC, CED be similar, respectively, to the triangles A'E'B', B'E'C', C'E'D'; and similarly placed.
Side 157 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Side 107 - ... of the regular inscribed and circumscribed polygons having double the number of sides. Let AB be a side of the given inscribed polygon ; EF, parallel to AB, a side of the circumscribed polygon ; C the centre of the circle. If the chord AM and the tangents AP, BQ, be drawn, AM...
Side 59 - Two triangles of the same altitude are to each other as their bases, and two triangles of the same base are to each other as their altitudes. And triangles generally, are to each other, as the products of their bases and altitudes.