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 TrigonometryW. E. Dean, 1842 - 317 páginas |
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Página 37
Containing the First Six Books of Euclid, with a Supplement on the Quadrature ... rectangle , equivalent to the triangle ABC ; and therefore the same construction will apply to the problem : to make a triangle equivalent to a given rectangle ...
Containing the First Six Books of Euclid, with a Supplement on the Quadrature ... rectangle , equivalent to the triangle ABC ; and therefore the same construction will apply to the problem : to make a triangle equivalent to a given rectangle ...
Página 38
Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids ... rectangle , having a side of a given length : for , if the angle D be a right angle , and AB the given side , the ...
Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids ... rectangle , having a side of a given length : for , if the angle D be a right angle , and AB the given side , the ...
Página 46
Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of ... length be found . COR . Since a triangle may be converted into an equivalent rectangle , it follows that any polygon ...
Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of ... length be found . COR . Since a triangle may be converted into an equivalent rectangle , it follows that any polygon ...
Página 47
Containing the First Six ... length , and draw BFD meeting the prolongation of AE in D ; then produce EF till FG is equal to HB : draw BGC , HFK , parallel to AED , and through the point D draw DKC parallel to AB or EG ; then , the rectangle ...
Containing the First Six ... length , and draw BFD meeting the prolongation of AE in D ; then produce EF till FG is equal to HB : draw BGC , HFK , parallel to AED , and through the point D draw DKC parallel to AB or EG ; then , the rectangle ...
Página 48
... rectangle contained by AD and DC , we shall simply say " the rectangle AD . DC , placing a point between the two sides of the " rectangle . " A. In Geometry , the product of two lines means the same thing as their rectangle , and this ...
... rectangle contained by AD and DC , we shall simply say " the rectangle AD . DC , placing a point between the two sides of the " rectangle . " A. In Geometry , the product of two lines means the same thing as their rectangle , and this ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore
Pasajes populares
Página 51 - 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.
Página 149 - IF an angle of a triangle be bisected by a straight line, which likewise cuts the base ; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of...
Página 12 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line.
Página 9 - 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 52 - 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.
Página 80 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Página 296 - 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 50 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Página 15 - 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.
Página 81 - If a straight line touch a circle, and from the point of contact a straight line be drawn cutting the circle, the angles made by...