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, 1853 - 317 σελίδες |
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Αποτελέσματα 1 - 5 από τα 68.
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 ...
Σελίδα 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 upon BA , AC . 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 upon BA , AC . On BC describe ( 46. 1 ...
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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 Let the straight 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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 74 - THE angles in the same segment of a circle are equal to one another...
Σελίδα 37 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Σελίδα 29 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Σελίδα 29 - 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 ; it is required to draw a straight line through EAF the point A, parallel to the straight line '
Σελίδα 147 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 19 - The angles which one straight line makes with another upon one side of i't, are either two right angles, or are together eqval to two right angles.
Σελίδα 134 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.
Σελίδα 294 - 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 13 - BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.