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 33
... reason the angle CAD has for its measure the half of ED ; therefore BAC + CAD , or BAD , has for its measure the half BE + ED , or the half of BD . Let us suppose , in the second place , that the centre C ( fig . 65 ) , Fig . 65 . is ...
... reason the angle CAD has for its measure the half of ED ; therefore BAC + CAD , or BAD , has for its measure the half BE + ED , or the half of BD . Let us suppose , in the second place , that the centre C ( fig . 65 ) , Fig . 65 . is ...
Σελίδα 43
... reason , DC AB , and FE AB ; therefore DC FE . If DC be taken from DE , there will remain CE ; and if FE , equal to DC , be taken also from DE , there will remain DF ; consequently CE = DF . = = Fig . 97 . Fig . 98 . Hence the Of the ...
... reason , DC AB , and FE AB ; therefore DC FE . If DC be taken from DE , there will remain CE ; and if FE , equal to DC , be taken also from DE , there will remain DF ; consequently CE = DF . = = Fig . 97 . Fig . 98 . Hence the Of the ...
Σελίδα 50
... reason ; consequently the triangles ABF , HBC , have two sides and the included angle of the one respectively equal to two sides and the included angle of the other ; they are therefore equal ( 36 ) . The triangle ABF is half of the ...
... reason ; consequently the triangles ABF , HBC , have two sides and the included angle of the one respectively equal to two sides and the included angle of the other ; they are therefore equal ( 36 ) . The triangle ABF is half of the ...
Σελίδα 58
... reason is , that all figures may be resolved into triangles , and any triangle whatever into two right - angled triangles . Thus the general properties of triangles involve those of all figures . THEOREM . 21 208. Two triangles , which ...
... reason is , that all figures may be resolved into triangles , and any triangle whatever into two right - angled triangles . Thus the general properties of triangles involve those of all figures . THEOREM . 21 208. Two triangles , which ...
Σελίδα 65
... reason the angle C = B ; therefore these triangles are similar , and the homologous sides give the proportion AO : DO :: CO : OB . 224. Corollary . Hence AO x OB DO × CO ; therefore the rectangle of the two parts of one of the chords is ...
... reason the angle C = B ; therefore these triangles are similar , and the homologous sides give the proportion AO : DO :: CO : OB . 224. Corollary . Hence AO x OB DO × CO ; therefore the rectangle of the two parts of one of the chords is ...
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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.