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 109
... proportional between the other two . X. When there is any number of magnitudes of the same kind , the first is said to have to the last the ratio compounded of the ratio which the first has to the second , and of the ratio which the ...
... proportional between the other two . X. When there is any number of magnitudes of the same kind , the first is said to have to the last the ratio compounded of the ratio which the first has to the second , and of the ratio which the ...
Σελίδα 124
... proportional to two sides of another , when one of the sides of the first is to one of the sides of the second , as the remaining side of the second is to the remaining side of the first . III . A straight line is said to be cut in ...
... proportional to two sides of another , when one of the sides of the first is to one of the sides of the second , as the remaining side of the second is to the remaining side of the first . III . A straight line is said to be cut in ...
Σελίδα 126
... proportionally : And if the sides , or the sides produced , be cut proportionally , the straight line which joins the points of sec- tion 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 sec- tion will be parallel to the remaining side of the triangle . Let DE be drawn parallel to BC , one of ...
Σελίδα 133
... proportional between the base and its segment adja- cent to that side . For in the triangles BDA , ADC , BD : DA :: DA : DC ( 4. 6. ) ; and in the trian- gles ABC , BDA , BC : BA :: BA : BD ( 4. 6. ) ; and in the trian- gles ABC , ACD ...
... proportional between the base and its segment adja- cent to that side . For in the triangles BDA , ADC , BD : DA :: DA : DC ( 4. 6. ) ; and in the trian- gles ABC , BDA , BC : BA :: BA : BD ( 4. 6. ) ; and in the trian- gles ABC , ACD ...
Σελίδα 134
... proportional , CE is found . Which was to be done . PROP . XII . D PROB . E To find a fourth proportional to three given straight lines . Let A , B , C he the three given straight lines ; it is required to find a fourth proportional to ...
... proportional , CE is found . Which was to be done . PROP . XII . D PROB . E To find a fourth proportional to three given straight lines . Let A , B , C he the three given straight lines ; it is required to find a fourth proportional to ...
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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.