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 páginas |
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Página 5
... square is that which has all its sides equal , and all its angles right angles . Book I. XXVI . An oblong is that which has all its angles right angles , but has not all its sides equal . XXVII . A rhombus is that which has all its ...
... square is that which has all its sides equal , and all its angles right angles . Book I. XXVI . An oblong is that which has all its angles right angles , but has not all its sides equal . XXVII . A rhombus is that which has all its ...
Página 45
... square upon a given straight line . Let AB be the given straight line ; it is required to de- scribe a square upon AB . EB C E d 34. 1 . From the point A drawa AC at right angles to AB , and a 11. 1 . makeb AD equal to AB , and through ...
... square upon a given straight line . Let AB be the given straight line ; it is required to de- scribe a square upon AB . EB C E d 34. 1 . From the point A drawa AC at right angles to AB , and a 11. 1 . makeb AD equal to AB , and through ...
Página 46
... square GB is double of the triangle BFC ; therefore the pa- rallelogram BL is equal to the square GB . In the same manner , by joining AE , BK , it may be demonstrated that the parallelogram CL is equal to the square HC . Therefore the ...
... square GB is double of the triangle BFC ; therefore the pa- rallelogram BL is equal to the square GB . In the same manner , by joining AE , BK , it may be demonstrated that the parallelogram CL is equal to the square HC . Therefore the ...
Página 47
... square described upon BC , one of the sides of the triangle ABC , be equal to the squares upon the other sides BA ... square of DA is equal to the square of AB . To each of these add the square of AC ; therefore the squares of DA , AC ...
... square described upon BC , one of the sides of the triangle ABC , be equal to the squares upon the other sides BA ... square of DA is equal to the square of AB . To each of these add the square of AC ; therefore the squares of DA , AC ...
Página 49
... square of a line , as AD , we N. 66 may sometimes write AD " , " " The sign + placed between the names of two magnitudes , signifies that those magnitudes are to be added together ; " and the sign - placed between them , signifies that ...
... square of a line , as AD , we N. 66 may sometimes write AD " , " " The sign + placed between the names of two magnitudes , signifies that those magnitudes are to be added together ; " and the sign - placed between them , signifies that ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle contained angle EDF arch base BC bisected Book centre circle ABC circumference coincide 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 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
Pasajes populares
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 3 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Página 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.
Página 160 - ... extremities of the base shall have the same ratio which the other sides of the triangle have to one...
Página 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.
Página 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.