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 |
Im Buch
Ergebnisse 1-5 von 100
Seite 5
... greater than a part of it ; or , the whole is equal to all its parts taken together ; or , two quantities that are each of them equal to a third quantity , are equal to each other . 5. A Theorem is a demonstrative proposition ; in which ...
... greater than a part of it ; or , the whole is equal to all its parts taken together ; or , two quantities that are each of them equal to a third quantity , are equal to each other . 5. A Theorem is a demonstrative proposition ; in which ...
Seite 6
... and is read A equal to B. 19. To signify that A is greater than B , the expression A7B is used . And to signify that A is less than B , the expression AB is used . 20. The sign of Addition is an erect cross ; 6 ELEMENTS.
... and is read A equal to B. 19. To signify that A is greater than B , the expression A7B is used . And to signify that A is less than B , the expression AB is used . 20. The sign of Addition is an erect cross ; 6 ELEMENTS.
Seite 11
... greater than its part . 10. All right angles are equal to one another . 11. " Two straight lines which intersect one another , cannot be both pa- " rallel to the same straight line . ” PROPOSITION I. PROBLEM . To describe an equilateral ...
... greater than its part . 10. All right angles are equal to one another . 11. " Two straight lines which intersect one another , cannot be both pa- " rallel to the same straight line . ” PROPOSITION I. PROBLEM . To describe an equilateral ...
Seite 13
... greater . It is required to cut off from AB , the greater , a part equai to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post . ) the ...
... greater . It is required to cut off from AB , the greater , a part equai to C , the less . From the point A draw ( 2. 1. ) the straight line AD equal to C ; and from the centre A , and at the distance AD , describe ( 3. Post . ) the ...
Seite 15
... greater than the other : Let AB be the greater , and from it cut ( 3. 1. ) off DB equal to AC the less , and 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 ...
... greater than the other : Let AB be the greater , and from it cut ( 3. 1. ) off DB equal to AC the less , and 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 ...
Andere Ausgaben - Alle anzeigen
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.