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 Sperical TrigonometryW.E. Dean, 1844 - 317 Seiten |
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Seite 8
... angle is the inclination of two straight lines to one another , which meet together , but are not in the same ... ABC , or CBA ; that which is contained by AB , * The definitions marked with inverted commas are different from those of Euclid ...
... angle is the inclination of two straight lines to one another , which meet together , but are not in the same ... ABC , or CBA ; that which is contained by AB , * The definitions marked with inverted commas are different from those of Euclid ...
Seite 13
... angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the ...
... angle ABC to the triangle DEF ; and the other an- gles , to which the equal sides are opposite , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the ...
Seite 14
... angle BAC is equal to the angle EDF ; wherefore also the point C shall ... ABC shall coincide with the whole triangle DEF , so that the spaces which ... angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two ...
... angle BAC is equal to the angle EDF ; wherefore also the point C shall ... ABC shall coincide with the whole triangle DEF , so that the spaces which ... angle ABC to the angle DEF , and the angle ACB to the angle DFE . Therefore , if two ...
Seite 15
... triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two ...
... triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon the other side of the base . COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two ...
Seite 16
... angle which is contain- ed by the two sides of the one shall be equal to the angle contained by the two sides of the other . Let ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each ...
... angle which is contain- ed by the two sides of the one shall be equal to the angle contained by the two sides of the other . Let ABC , DEF be two triangles having the two sides AB , AC , equal to the two sides DE , DF , each to each ...
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Häufige Begriffe und Wortgruppen
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
Beliebte Passagen
Seite 95 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Seite 68 - THE angles in the same segment of a circle are equal to one another...
Seite 23 - 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.
Seite 74 - 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.
Seite 78 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Seite 9 - 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.
Seite 75 - If a straight line touch a circle, and from the point of contact a...
Seite 18 - AT a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A...
Seite 134 - EQUIANGULAR parallelograms have to one another the ratio which is compounded of the ratios of their sides.
Seite 136 - AB is (7. 5.) to AD, as AE to AG ; and DC to CB, as GF to FE; and also CD to DA, as FG to GA ; therefore the sides of the parallelograms ABCD, AEFG about the equal angles are proportionals; and they are therefore similar to one another (1.