Elements of GeometryHilliard and Metcalf, 1825 - 224 σελίδες |
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Σελίδα v
... given points . For , from this essential property we can deduce all the other properties of a straight line , and particularly that of its being the shortest be- tween two given points . But in order to this it would have been necessary ...
... given points . For , from this essential property we can deduce all the other properties of a straight line , and particularly that of its being the shortest be- tween two given points . But in order to this it would have been necessary ...
Σελίδα vii
... given two methods of approximation for squaring the circle , one of which is that of James Gregory . This section is followed by an appendix , in which we have de- monstrated that the circle is greater than any rectilineal figure of the ...
... given two methods of approximation for squaring the circle , one of which is that of James Gregory . This section is followed by an appendix , in which we have de- monstrated that the circle is greater than any rectilineal figure of the ...
Σελίδα 3
... given indifferently to theorems , problems , and lemmas . A Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a remark upon one or more propositions which have gone before , tending to show ...
... given indifferently to theorems , problems , and lemmas . A Corollary is a consequence which follows from one or sev- eral propositions . A Scholium is a remark upon one or more propositions which have gone before , tending to show ...
Σελίδα 11
... given point A ( fig . 31 ) , without a straight line DE , Fig 31 . only one perpendicular can be drawn to that line . Demonstration . If it be possible , let there be two AB and AC ; produce one of them AB , so that BF = AB . and join ...
... given point A ( fig . 31 ) , without a straight line DE , Fig 31 . only one perpendicular can be drawn to that line . Demonstration . If it be possible , let there be two AB and AC ; produce one of them AB , so that BF = AB . and join ...
Σελίδα 12
... given straight line ; for , if this could be done , there would be on the same side of the perpendicular two equal oblique lines , which is impossible . Fig . 32 . THEOREM . 55. If from the point C ( fig . 32 ) , the middle of the ...
... given straight line ; for , if this could be done , there would be on the same side of the perpendicular two equal oblique lines , which is impossible . Fig . 32 . THEOREM . 55. If from the point C ( fig . 32 ) , the middle of the ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 65 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 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.
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 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'.
Σελίδα 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.
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 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.
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.
Σελίδα 24 - In the same circle, or in equal circles, equal arcs are subtended by equal chords ; and, conversely, equal chords subtend equal arcs.
Σελίδα 153 - XVII.) ; hence two similar pyramids are to each other as the cubes of their homologous sides.