Elements of Geometry and Trigonometry: With NotesJ. Ryan, 1828 - 316 σελίδες |
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Σελίδα xi
... evident that BB ' , D - D ' , may approximate to B and D , as near as we please ; and since the proportion still continues accurate at every successive approximation , we infer that it will , in like manner , continue accurate at the ...
... evident that BB ' , D - D ' , may approximate to B and D , as near as we please ; and since the proportion still continues accurate at every successive approximation , we infer that it will , in like manner , continue accurate at the ...
Σελίδα 4
... evident proposition . A theorem is a truth , which becomes evident by means of a train of reasoning called a demonstration . A problem is a question proposed , which requires a solu- tion . A lemma is a subsidiary truth , employed for ...
... evident proposition . A theorem is a truth , which becomes evident by means of a train of reasoning called a demonstration . A problem is a question proposed , which requires a solu- tion . A lemma is a subsidiary truth , employed for ...
Σελίδα 7
... evident that the two lines must coincide entirely between A and B , for otherwise there would be two straight lines between A A B C D and B , which is impossible ( 25. ) . Suppose , however , that on being produced , these lines begin ...
... evident that the two lines must coincide entirely between A and B , for otherwise there would be two straight lines between A A B C D and B , which is impossible ( 25. ) . Suppose , however , that on being produced , these lines begin ...
Σελίδα 10
... ; but we have found GC = EF , therefore , EF / BC . Second Case . If the point G fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC . B CE F Third Case . Lastly , if the point G fall 10 GEOMETRY .
... ; but we have found GC = EF , therefore , EF / BC . Second Case . If the point G fall on the side BC , it is evident that GC , or its equal EF , will be shorter than BC . B CE F Third Case . Lastly , if the point G fall 10 GEOMETRY .
Σελίδα 23
... evident , also , that the sum of all the angles in those triangles does not differ from the sum of all the angles in the polygon : hence the latter sum is equal to as many times two right angles as there are triangles in the figure ; in ...
... evident , also , that the sum of all the angles in those triangles does not differ from the sum of all the angles in the polygon : hence the latter sum is equal to as many times two right angles as there are triangles in the figure ; in ...
Άλλες εκδόσεις - Προβολή όλων
Elements Of Geometry And Trigonometry From The Works Of A.m. Legendre Adrien Marie Legendre Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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...
Σελίδα 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...
Σελίδα 3 - A right-angled triangle is one which has a right angle. The side opposite the right angle is called the hypothenuse.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.