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 62
... segment is the angle contained by two straight lines drawn from any point in the circumference of the segment , to the extre- mities of the straight line which is the base of the segment . An inscribed triangle , is one which has its ...
... segment is the angle contained by two straight lines drawn from any point in the circumference of the segment , to the extre- mities of the straight line which is the base of the segment . An inscribed triangle , is one which has its ...
Página 75
... segment of a circle are equal to one another . Let ABCD be a circle , and BAD , BED angles in the same segment BAED : the an- gles BAD , BED are equal to one another . Take F the centre of the circle ABCD : And , first , let the segment ...
... segment of a circle are equal to one another . Let ABCD be a circle , and BAD , BED angles in the same segment BAED : the an- gles BAD , BED are equal to one another . Take F the centre of the circle ABCD : And , first , let the segment ...
Página 76
... segments of circles upon the equal straight lines AB , CD ; the segment AEB is equal to the segment CFD . For , if the segment AEB be applied to the segment CFD , so as the point A be on C , and the straight line AB upon CD , the point ...
... segments of circles upon the equal straight lines AB , CD ; the segment AEB is equal to the segment CFD . For , if the segment AEB be applied to the segment CFD , so as the point A be on C , and the straight line AB upon CD , the point ...
Página 77
... segment B B A D B Α ' C E A E D C is described and because the centre D is in AC , the segment ABC is a semicircle . Next , let the angles ABD , BAD be unequal ; at the point A , in the straight line AB , make ( 23. 1. ) the angle BAE ...
... segment B B A D B Α ' C E A E D C is described and because the centre D is in AC , the segment ABC is a semicircle . Next , let the angles ABD , BAD be unequal ; at the point A , in the straight line AB , make ( 23. 1. ) the angle BAE ...
Página 78
... segment BAC is similar ( 9. def . 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore the segment BAC is ...
... segment BAC is similar ( 9. def . 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore the segment BAC is ...
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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...