Elements of Geometry and Plane Trigonometry: With an Appendix, and Copious Notes and IllustrationsA. Constable & Company, 1817 - 432 Seiten |
Im Buch
Ergebnisse 1-5 von 100
Seite 5
... BC , or the opening formed by turning BA about the point B into the position BC , is named ABC or CBA . A- 4. A ... equal to each other . If a straight line CB stand at equal angles CBA and CBD on another straight line AD , and if the ...
... BC , or the opening formed by turning BA about the point B into the position BC , is named ABC or CBA . A- 4. A ... equal to each other . If a straight line CB stand at equal angles CBA and CBD on another straight line AD , and if the ...
Seite 14
... equal , if two sides and the angle contained by these in the one be respective- ly equal to two sides and the contained angle in the other . Let ABC and DEF be two triangles , of which the side AB is equal to DE , the side BC to EF ...
... equal , if two sides and the angle contained by these in the one be respective- ly equal to two sides and the contained angle in the other . Let ABC and DEF be two triangles , of which the side AB is equal to DE , the side BC to EF ...
Seite 15
... equal to a given angle . At the point D in the given straight line DE , to form an angle equal to the given angle ... BC and BA equal to its sides , and the base AC being repeatedly inserted be- tween those circumferences ; a multi- tude ...
... equal to a given angle . At the point D in the given straight line DE , to form an angle equal to the given angle ... BC and BA equal to its sides , and the base AC being repeatedly inserted be- tween those circumferences ; a multi- tude ...
Seite 16
... BC of the given angle be supposed equal , only one circle would be required , a series of equal isosceles triangles being constituted about its centre . It is evi- dent that this addition is without limit , and that the angle so ...
... BC of the given angle be supposed equal , only one circle would be required , a series of equal isosceles triangles being constituted about its centre . It is evi- dent that this addition is without limit , and that the angle so ...
Seite 18
... equal to BC and BD of the triangle CBD , and the side CD common to them both ; these triangles ( I. 2. ) are equal , and the angle ACD or ACE is equal to BCD or BCE . Again , B E the inferior triangles ACE and BCE , having the side AC equal ...
... equal to BC and BD of the triangle CBD , and the side CD common to them both ; these triangles ( I. 2. ) are equal , and the angle ACD or ACE is equal to BCD or BCE . Again , B E the inferior triangles ACE and BCE , having the side AC equal ...
Andere Ausgaben - Alle anzeigen
Elements of Geometry, and Plane Trigonometry: With an Appendix, and Very ... University Professor Emeritus John Leslie, Sir Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD adjacent angle altitude angle ABC angle ADB angle BAC base AC bisect centre chord circle circumference consequently construction contained angle cosine decagon denote describe diameter difference distance diverging lines divided draw equal to BC equilateral triangle equivalent to twice evidently exterior angle Geometry given greater half Hence hypotenuse inscribed isosceles triangle join let fall likewise measure parallel perpendicular point G polygon PROB PROP Proposition quadrilateral figure quantities radius ratio rectangle rectangle contained rectilineal figure rhomboid right angles right-angled triangle Scholium segments semicircle semiperimeter side AC sides AB sinB sine square of AB square of AC straight line tangent THEOR tion triangle ABC twice the rectangle twice the square vertex vertical angle whence Wherefore
Beliebte Passagen
Seite 22 - THEOR. Two sides of a triangle are together greater than the third side. The two sides AB and BC of the triangle ABC are together greater than the third side AC. For produce AB until DB be equal to the side BC, and join CD. Because BC is equal to BD, the angle BCD is equal to BDC (I.
Seite 292 - axiom, (If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles, these straight lines, being continually produced, will at length meet on that side on which are the angles which are less
Seite 10 - circumference. 35. The diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. It is obvious that all radii of the same circle are equal to each other and to a
Seite 50 - PROB. With a given straight line to construct a rhomboid equivalent to a given rectilineal figure, and having an angle equal to a given angle. Let it be required to construct, with the straight line L, a rhomboid, containing a given space, and having an angle equal to K. Construct (II.
Seite 144 - Proposition is named inverse, or perturbate, equality. PROP. XIX. THEOR. If there be any number of proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents. .
Seite 236 - &c. &c. PROP. IV. THEOR. The sum of the sines of two arcs is to their difference, as the tangent of half the sum of those arcs to the tangent of half
Seite 110 - Hence a regular twenty-sided figure may be described on a given straight line, by first constructing on it an isosceles triangle having each of the angles at the base double of the vertical angle,
Seite 30 - THEOR. If a straight line fall upon two parallel straight lines, it will make the alternate angles equal, the exterior angle equal to the interior opposite one, and the two interior angles on the same side together equal to two right angles. • Let the straight line EFG fall upon the parallels AB and CD ; the alternate angles AGF and DFG are equal, the
Seite 137 - founded the two following theorems. PROP. VII. THEOR. The terms of an analogy are proportional by inversion, or the second is to the first, as the fourth to the third. Let A : B : : C : D ; then inversely B : A : : D : C.
Seite 88 - THEOR. The angle in a semicircle is a right angle, the angle in a greater segment is acute, and the angle in a smaller segment is obtuse. Let ABD be an angle in a semicircle, or that stands on the semicircumference AED; it is a right angle.