Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of SolidsF. Nichols, 1806 - 311 σελίδες |
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Αποτελέσματα 1 - 5 από τα 43.
Σελίδα 132
... proportional between the other two . Χ . N. When there is any number of magnitudes of the same kind , the first is said to have to the last of them the ratio com- pounded of the ratio which the first has to the second , and of the ratio ...
... proportional between the other two . Χ . N. When there is any number of magnitudes of the same kind , the first is said to have to the last of them the ratio com- pounded of the ratio which the first has to the second , and of the ratio ...
Σελίδα 155
... proportional . I. Book VI . II . Two sides of one figure are said to be reciprocally propor tional to two sides of another , when one of the sides of the first is to one of the sides of the other , as the remaining side of the other is ...
... proportional . I. Book VI . II . Two sides of one figure are said to be reciprocally propor tional to two sides of another , when one of the sides of the first is to one of the sides of the other , as the remaining side of the other is ...
Σελίδα 157
... proportionally ; and if the sides , or the sides produced , be cut proportionally , the straight line which joins the points of section will be parallel to the remaining side of the triangle . Let DE be drawn parallel to BC , one of ...
... proportionally ; and if the sides , or the sides produced , be cut proportionally , the straight line which joins the points of section will be parallel to the remaining side of the triangle . Let DE be drawn parallel to BC , one of ...
Σελίδα 158
... proportionally in the points D , E , that is , so that BD be to DA , as CE to EA ; and join DE ; DE is parallel to BС . The same construction being made , as BD to DA , so is CE to EA , and as BD to DA , so is the triangle BDE to the ...
... proportionally in the points D , E , that is , so that BD be to DA , as CE to EA ; and join DE ; DE is parallel to BС . The same construction being made , as BD to DA , so is CE to EA , and as BD to DA , so is the triangle BDE to the ...
Σελίδα 161
... proportional ; and those which are op- posite to the equal angles are homologous sides , that is , are the antecedents or consequents of the ratios . Let ABC , DCE be equiangular triangles , having the angle ABC equal to the angle DCE ...
... proportional ; and those which are op- posite to the equal angles are homologous sides , that is , are the antecedents or consequents of the ratios . Let ABC , DCE be equiangular triangles , having the angle ABC equal to the angle DCE ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal altitude angle ABC angle ACB angle BAC angle contained angle EDF arch base BC bisected Book centre circle ABC circumference coincide common section cylinder definition demonstrated diameter draw drawa equal angles equiangular equilateral polygon equimultiples Euclid exterior angle fore four right angles given circle given straight line greater inscribed interior and opposite join less Let ABC Let the straight meet multiple opposite angle parallelogram parallelogram ABCD perpendicular point F polygon prism PROB produced proportional proposition pyramid Q. E. D. COR Q. E. D. PROP ratio rectangle contained rectilineal figure remaining angle segment solid angle solid parallelepipeds straight line AB straight line AC Suppl THEOR third touches the circle triangle ABC triangle DEF
Δημοφιλή αποσπάσματα
Σελίδα 121 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 42 - TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 63 - Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.
Σελίδα 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Σελίδα 183 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides.
Σελίδα 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Σελίδα 291 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Σελίδα 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...
Σελίδα 10 - ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz.
Σελίδα 14 - Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal to one another.