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 131
... fourth , equal to it , or less ; then the first of the magnitudes is said to have to the second the same ratio that the third has to the fourth . VI . Magnitudes are said to be proportionals , when the first has the same ratio to the ...
... fourth , equal to it , or less ; then the first of the magnitudes is said to have to the second the same ratio that the third has to the fourth . VI . Magnitudes are said to be proportionals , when the first has the same ratio to the ...
Página 132
... fourth , and so on unto the last magnitude . For example , if A , B , C , D be four magnitudes of the same kind , the first A is said to have to the last D the ratio com- pounded of the ratio of A to B , and of the ratio of B to C , and ...
... fourth , and so on unto the last magnitude . For example , if A , B , C , D be four magnitudes of the same kind , the first A is said to have to the last D the ratio com- pounded of the ratio of A to B , and of the ratio of B to C , and ...
Página 133
... fourth ; or that the first is to the third as the second to the fourth . See prop . 16th of this book . Book V. XV . Invertendo , by inversion : when there are four proportionals , and it is inferred , that the second is to the first as ...
... fourth ; or that the first is to the third as the second to the fourth . See prop . 16th of this book . Book V. XV . Invertendo , by inversion : when there are four proportionals , and it is inferred , that the second is to the first as ...
Página 134
... fourth is to the fourth . 17th prop . book 5 . XVIII . Convertendo , by conversion : when there are four propor- tionals , and it is inferred , that the first is to its excess above the second , as the third to its excess above the ...
... fourth is to the fourth . 17th prop . book 5 . XVIII . Convertendo , by conversion : when there are four propor- tionals , and it is inferred , that the first is to its excess above the second , as the third to its excess above the ...
Página 135
... fourth of the first rank , so is the Book V. third from the last to the last but two of the second rank ; and so on in a cross , or inverse , order ; and the inference is as in the 19th definition . It is demonstrated in the 23d prop ...
... fourth of the first rank , so is the Book V. third from the last to the last but two of the second rank ; and so on in a cross , or inverse , order ; and the inference is as in the 19th definition . It is demonstrated in the 23d prop ...
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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.