Elements of Geometry: Containing the First Six Books of Euclid : with a Supplement on the Quadrature of the Circle, and the Geometry of Solids : to which are Added Elements of Plane and Spherical TrigonometryPrinted and published at no. 24 Arch Street, A. Walker, Agent, 1832 - 333 σελίδες |
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Σελίδα ix
... divided , treats of the rectification and quadrature of the circle , ― subjects that are of- ten omitted altogether in works of this kind . They are omitted , however , as I conceive , without any good reason , because , to mea- sure ...
... divided , treats of the rectification and quadrature of the circle , ― subjects that are of- ten omitted altogether in works of this kind . They are omitted , however , as I conceive , without any good reason , because , to mea- sure ...
Σελίδα xiii
... divided , that the part of it that is barely sufficient for the re- solution of Triangles may be easily taught by itself . The method of constructing the Trigonometrical Tables is explained , and a de- monstration is added of those ...
... divided , that the part of it that is barely sufficient for the re- solution of Triangles may be easily taught by itself . The method of constructing the Trigonometrical Tables is explained , and a de- monstration is added of those ...
Σελίδα 28
... divided into two equal parts in the point D. Which was to be done . A D B PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in that line . F Let AB be a given straight line and C a ...
... divided into two equal parts in the point D. Which was to be done . A D B PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in that line . F Let AB be a given straight line and C a ...
Σελίδα 42
... divided into as many triangles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by the preced- ing proposition , all the angles of these tri- angles are equal to twice as ...
... divided into as many triangles as the figure has sides , by drawing straight lines from a point F within the figure to each of its angles . And , by the preced- ing proposition , all the angles of these tri- angles are equal to twice as ...
Σελίδα 54
... divided into any number of parts ; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line and the several parts of the divided line . Let A and BC be two straight lines ; and let BC ...
... divided into any number of parts ; the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line and the several parts of the divided line . Let A and BC be two straight lines ; and let BC ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism PROB proportional proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelopipeds spherical angle spherical triangle SPHERICAL TRIGONOMETRY square straight line AC THEOR third touches the circle triangle ABC wherefore
Δημοφιλή αποσπάσματα
Σελίδα 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 41 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Σελίδα 36 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 33 - ANY two sides of a triangle are together greater than the third side.
Σελίδα 19 - 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 308 - 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 25 - 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 extremity...
Σελίδα 56 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Σελίδα 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 90 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.