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 100.
Σελίδα 14
... join FC , GB . A Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG com- mon to the two triangles , AFC , AGB ; therefore the base FC is equal ...
... join FC , GB . A Because AF is equal to AG , and AB to AC , the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG com- mon to the two triangles , AFC , AGB ; therefore the base FC is equal ...
Σελίδα 15
... join DC ; therefore , because in the tri- angles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore ...
... join DC ; therefore , because in the tri- angles DBC , ACB , DB is equal to AC , and BC common to both , the two sides DB , BC are equal to the two AC , CB , each to each ; but the angle DBC is also equal to the angle ACB ; therefore ...
Σελίδα 17
... join DE , and upon it describe ( 1.1 . ) an equilateral triangle DEF ; then join AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is com- mon to the two triangles DAF , EAF ; the two sides DA , AF ...
... join DE , and upon it describe ( 1.1 . ) an equilateral triangle DEF ; then join AF ; the straight line AF bisects the angle BAC . Because AD is equal to AE , and AF is com- mon to the two triangles DAF , EAF ; the two sides DA , AF ...
Σελίδα 18
... join FC ; the straight line FC , drawn from the giv- en point C , is at right angles to the given straight line AB . A D C E B Because DC is equal to CE , and FC common to the two triangles DCF , ECF , the two sides DC , CF are equal to ...
... join FC ; the straight line FC , drawn from the giv- en point C , is at right angles to the given straight line AB . A D C E B Because DC is equal to CE , and FC common to the two triangles DCF , ECF , the two sides DC , CF are equal to ...
Σελίδα 20
... join BE and produce it to F , and make El equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal ( 15. 1. ) to the angle CEF ...
... join BE and produce it to F , and make El equal to BE ; join also FC , and produce AC to G. Because AE is equal to EC , and BE to EF ; AE , EB are equal to CE , EF , each to each ; and the angle AEB is equal ( 15. 1. ) to the angle CEF ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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.