Elements of Geometry |
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Σελίδα 163
But EH + GF is the same as EF + GH ; therefore the arc GH , which measures the
angle A , is equal to a semicircumference minus the side EF ; likewise the angle
B has for its measure į circ . — DF , and the angle C , 4 circ . - DE . This property ...
But EH + GF is the same as EF + GH ; therefore the arc GH , which measures the
angle A , is equal to a semicircumference minus the side EF ; likewise the angle
B has for its measure į circ . — DF , and the angle C , 4 circ . - DE . This property ...
Σελίδα 180
258 ) be the radius of the base of the given cylinder , H its altitude ; and let circ .
CA be the circumference of a circle whose radius is CA ; we say that circ . CA * H
will be the convex surface of the cylinder . For , if this proposition be denied , circ .
258 ) be the radius of the base of the given cylinder , H its altitude ; and let circ .
CA be the circumference of a circle whose radius is CA ; we say that circ . CA * H
will be the convex surface of the cylinder . For , if this proposition be denied , circ .
Σελίδα 181
CA X H. But circ . CA X H is , by hypothesis , the convex surface of a cylinder of
which CD is the radius of the base , which cylinder is inscribed in the prism ;
whence the convex surface of the prism would be less than that of the inscribed ...
CA X H. But circ . CA X H is , by hypothesis , the convex surface of a cylinder of
which CD is the radius of the base , which cylinder is inscribed in the prism ;
whence the convex surface of the prism would be less than that of the inscribed ...
Σελίδα 184
259 ) , be the radius of the base of the given cone , S its vertex , and SA its side ;
we say that the surface will be circ . AOR SA . For , if it be possible , let circ . AO * Į
SA be the surface of a cone which has S for its vertex , and for its base the circle ...
259 ) , be the radius of the base of the given cone , S its vertex , and SA its side ;
we say that the surface will be circ . AOR SA . For , if it be possible , let circ . AO * Į
SA be the surface of a cone which has S for its vertex , and for its base the circle ...
Σελίδα 185
We say also , that this same product cannot be thc measure of the surface of a
less cone , For let BO be the radius of the base of the given cone , and , if it be
possible , let circ . BOX { SB be the surface of a cone of which S is the vertex , and
AO ...
We say also , that this same product cannot be thc measure of the surface of a
less cone , For let BO be the radius of the base of the given cone , and , if it be
possible , let circ . BOX { SB be the surface of a cone of which S is the vertex , and
AO ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD adjacent altitude angle ACB applied base called centre chord circ circle circumference circumscribed common comprehended cone consequently considered construction contained Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces figure follows formed four give given greater half hence homologous sides inclination inscribed join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles pole polyedron polygon prism PROBLEM proportional proposition pyramid radii radius ratio reason rectangle regular polygon remain respect right angles Scholium sector segment side BC similar solid angle Solution sphere spherical triangle square straight line suppose surface taken THEOREM third triangle ABC vertex vertices whence
Δημοφιλή αποσπάσματα
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.