The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five BooksA. & C. Black, 1837 - 390 páginas |
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... to practical purposes . In this are given the best methods at present known for the resolution of plane triangles , and the application of trigonometry in deter- mining heights and distances in some of the simplest and iv PREFACE .
... to practical purposes . In this are given the best methods at present known for the resolution of plane triangles , and the application of trigonometry in deter- mining heights and distances in some of the simplest and iv PREFACE .
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... method of investigation requiring a knowledge of algebraic operations , which , in the rest of the volume , the student is not supposed to possess . Any person , therefore , who wishes to study spherical trigonometry , or even plane ...
... method of investigation requiring a knowledge of algebraic operations , which , in the rest of the volume , the student is not supposed to possess . Any person , therefore , who wishes to study spherical trigonometry , or even plane ...
Página 5
... method of performing it to be known . The method of solving all other problems that occur in the work , is pointed out . An axiom is a self - evident theorem ; -that is , a theorem , the truth of which the human mind is so constituted ...
... method of performing it to be known . The method of solving all other problems that occur in the work , is pointed out . An axiom is a self - evident theorem ; -that is , a theorem , the truth of which the human mind is so constituted ...
Página 9
... method , however , though greatly preferable in practice , could not in strictness be adopted by Euclid , as it is not derived from the postulates or the first proposition . It is in fact , the same as assuming this proposition as a ...
... method , however , though greatly preferable in practice , could not in strictness be adopted by Euclid , as it is not derived from the postulates or the first proposition . It is in fact , the same as assuming this proposition as a ...
Página 11
... be equal for a like reason . When a proposition is demonstrated by supposing one figure to be applied to another , it is said to be proved by the method of superposition . PROP . V. THEOR . THE angles at the base Book I. ] 11 OF EUCLID .
... be equal for a like reason . When a proposition is demonstrated by supposing one figure to be applied to another , it is said to be proved by the method of superposition . PROP . V. THEOR . THE angles at the base Book I. ] 11 OF EUCLID .
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore
Pasajes populares
Página 94 - 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.
Página 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Página 143 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Página 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Página 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Página 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Página 32 - 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 40 - 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 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...