Elements of Geometry...: Translated from the French for the Use of the Students of the University at Cambridge, New EnglandHilliard and Metcalf, 1825 - 224 σελίδες |
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Σελίδα 21
... consequently the side AD is parallel to BC ( 67 ) . For a similar reason AB is parallel to CD ; there- fore the quadrilateral ABCD is a parallelogram . THEOREM . 1 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig ...
... consequently the side AD is parallel to BC ( 67 ) . For a similar reason AB is parallel to CD ; there- fore the quadrilateral ABCD is a parallelogram . THEOREM . 1 87. If two opposite sides AB , CD ( fig . 44 ) , of a quadrilateral Fig ...
Σελίδα 38
... consequently be the greatest of the sides . 2. If the angle C ( fig . 81 ) is acute , and B greater than A , the construction is the same , and DEF is the triangle required . But if , while C ( fig . 82 ) is acute , the side B is less ...
... consequently be the greatest of the sides . 2. If the angle C ( fig . 81 ) is acute , and B greater than A , the construction is the same , and DEF is the triangle required . But if , while C ( fig . 82 ) is acute , the side B is less ...
Σελίδα 39
... , OE , OF , to the three sides of the triangle ; these lines will be equal to each other . For , by construc- tion , the angle DAO = OAF , and the right angle ADO = AFO ; Fig . 88 , 89 . consequently the third angle Problems . 39.
... , OE , OF , to the three sides of the triangle ; these lines will be equal to each other . For , by construc- tion , the angle DAO = OAF , and the right angle ADO = AFO ; Fig . 88 , 89 . consequently the third angle Problems . 39.
Σελίδα 40
... consequently the third angle AOD is equal to the third AOF . Besides , the side AO is common to the two triangles AOD , AOF ; therefore , a side and the adjacent angles of the one being respec- tively equal to a side and the adjacent ...
... consequently the third angle AOD is equal to the third AOF . Besides , the side AO is common to the two triangles AOD , AOF ; therefore , a side and the adjacent angles of the one being respec- tively equal to a side and the adjacent ...
Σελίδα 45
... consequently it is equal to AE . Whatever therefore be the ratio of the bases , two rectangles ABCD , AEFD , of the same altitude , are to each other as their bases AB , AE . THEOREM . 172. Any two rectangles ABCD , AEGF ( fig . 101 ) ...
... consequently it is equal to AE . Whatever therefore be the ratio of the bases , two rectangles ABCD , AEFD , of the same altitude , are to each other as their bases AB , AE . THEOREM . 172. Any two rectangles ABCD , AEGF ( fig . 101 ) ...
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Elements of Geometry...: Translated from the French for the Use of the ... Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2020 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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 geometry 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 triangular prism triangular pyramids vertex vertices whence
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Σελίδα 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...
Σελίδα 9 - 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.
Σελίδα 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 9 - Hence a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts.
Σελίδα 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...
Σελίδα 61 - 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'.
Σελίδα 166 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 153 - 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 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Σελίδα 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.