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 11
... described from any centre , at any distance from that centre . AXIOMS . 1. THINGS which are equal to the same thing are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If equals be taken from equals ...
... described from any centre , at any distance from that centre . AXIOMS . 1. THINGS which are equal to the same thing are equal to one another . 2. If equals be added to equals , the wholes are equal . 3. If equals be taken from equals ...
Página 12
... described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line ; it is required to draw , from the ...
... described upon the given straight line AB . PROP . II . PROB . From a given point to draw a straight line equal to a given straight line . Let A be the given point , and BC the given straight line ; it is required to draw , from the ...
Página 37
... described a parallelogram FECG equal to a given triangle ABC , having one of its angles CEF equal to the given angle D. COR . Hence , if the angle D be a right angle , the parallelogram EFGC will be a rectangle , equivalent to the ...
... described a parallelogram FECG equal to a given triangle ABC , having one of its angles CEF equal to the given angle D. COR . Hence , if the angle D be a right angle , the parallelogram EFGC will be a rectangle , equivalent to the ...
Página 39
... described equal to the given rectilineal figure ABCD , hav- ing the angle FKM equal to the given angle E. COR . From this it is manifest how to a given straight line to apply a parallelogram , which shall have an angle equal to a given ...
... described equal to the given rectilineal figure ABCD , hav- ing the angle FKM equal to the given angle E. COR . From this it is manifest how to a given straight line to apply a parallelogram , which shall have an angle equal to a given ...
Página 40
... described upon the sides which contain the right angle . Let ABC be a right angled triangle having the right angle BAC ; the square described upon the side BC is equal to the squares described BA , AC . upon On BC describe ( 46. 1 ...
... described upon the sides which contain the right angle . Let ABC be a right angled triangle having the right angle BAC ; the square described upon the side BC is equal to the squares described BA , AC . upon On BC describe ( 46. 1 ...
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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...