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 TrigonometryJ.B. Lippincott, 1857 - 317 σελίδες |
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Σελίδα 7
... half of the line AB . 25. Division , or the ratio of one quantity to another , is usually denoted by placing one of the two quantities over the other , in the form of a fraction : A B thus , signifies the ratio or quotient arising from ...
... half of the line AB . 25. Division , or the ratio of one quantity to another , is usually denoted by placing one of the two quantities over the other , in the form of a fraction : A B thus , signifies the ratio or quotient arising from ...
Σελίδα 35
... half of the parallelogram EBCA , because the diameter AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it ; and the halves of equal things are equal ( 7 . Ax ...
... half of the parallelogram EBCA , because the diameter AB bisects ( 34. 1. ) it ; and the triangle DBC is the half of the parallelogram DBCF , because the diameter DC bisects it ; and the halves of equal things are equal ( 7 . Ax ...
Σελίδα 51
... half the line . Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts in the point D ; the rectangle AD.DB , together with the square of CD , is equal to the square of CB , or AD.DB + CD2 ...
... half the line . Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts in the point D ; the rectangle AD.DB , together with the square of CD , is equal to the square of CB , or AD.DB + CD2 ...
Σελίδα 52
... half the line bisected , is equal to the square of the straight line which is made up of the half and the part produced . Let the straight line AB be bisected in C , and produced to the point D ; the rectangle AD.DB together with the ...
... half the line bisected , is equal to the square of the straight line which is made up of the half and the part produced . Let the straight line AB be bisected in C , and produced to the point D ; the rectangle AD.DB together with the ...
Σελίδα 54
... half that line . " 66 SCHOLIUM . In this proposition , let the line AB be denoted by a , and the parts AC and CB by c and b ; then AD = c + 2b . Now , since a = b + c , multiplying both members by 4b , we shall have 4ab = 4b2 + 4bc ...
... half that line . " 66 SCHOLIUM . In this proposition , let the line AB be denoted by a , and the parts AC and CB by c and b ; then AD = c + 2b . Now , since a = b + c , multiplying both members by 4b , we shall have 4ab = 4b2 + 4bc ...
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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 plane 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 third touches the circle triangle ABC triangle DEF wherefore