The Elements of Euclid for the Use of Schools and Colleges: Comprising the First Six Books and Portions of the Eleventh and Twelfth Books : with Notes, an Appendix, and ExercisesMacmillan, 1883 - 400 Seiten |
Im Buch
Ergebnisse 1-5 von 72
Seite 5
... . That a terminated straight line may be produced to any length in a straight line : 3. And that a circle may be described from any centre , at any distance from that centre AXIOMS . 1. Things which are equal to the same DEFINITIONS . 5.
... . That a terminated straight line may be produced to any length in a straight line : 3. And that a circle may be described from any centre , at any distance from that centre AXIOMS . 1. Things which are equal to the same DEFINITIONS . 5.
Seite 7
... CA , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , [ Axiom 1 . [ Def . 24 . and it is described on the given straight line AB . Q.E.F. PROPOSITION 2. PROBLEM . From a given point to draw.
... CA , AB , BC are equal to one another . Wherefore the triangle ABC is equilateral , [ Axiom 1 . [ Def . 24 . and it is described on the given straight line AB . Q.E.F. PROPOSITION 2. PROBLEM . From a given point to draw.
Seite 49
... described on the given straight line AB . Q.E.F. COROLLARY . From the demonstration it is manifest that every parallelogram which has one right angle has all its angles right angles . PROPOSITION 47. THEOREM . In any right - angled ...
... described on the given straight line AB . Q.E.F. COROLLARY . From the demonstration it is manifest that every parallelogram which has one right angle has all its angles right angles . PROPOSITION 47. THEOREM . In any right - angled ...
Seite 50
... described on the sides which contain the right angle . Let ABC be a right - angled triangle , having the right angle BAC : the square described on the side BC shall be equal to the squares described on the sides BA , AC . On BC describe ...
... described on the sides which contain the right angle . Let ABC be a right - angled triangle , having the right angle BAC : the square described on the side BC shall be equal to the squares described on the sides BA , AC . On BC describe ...
Seite 51
... described on BC , and the squares GB , HC on BA , AC . Therefore the square described on the side BC is equal to the squares described on the sides BA , AC . Wherefore , in any right - angled triangle & c . Q.E.D. PROPOSITION 48 ...
... described on BC , and the squares GB , HC on BA , AC . Therefore the square described on the side BC is equal to the squares described on the sides BA , AC . Wherefore , in any right - angled triangle & c . Q.E.D. PROPOSITION 48 ...
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
ABCD AC is equal angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC bisects the angle centre chord circle ABC circle described circumference Construction Corollary describe a circle diameter double draw a straight equal angles equal to F equiangular equilateral equimultiples Euclid Euclid's Elements exterior angle given circle given point given straight line gnomon Hypothesis inscribed intersect isosceles triangle less Let ABC magnitudes middle point multiple opposite angles opposite sides parallelogram perpendicular plane polygon produced proportionals PROPOSITION 13 Q.E.D. PROPOSITION quadrilateral radius rectangle contained rectilineal figure remaining angle rhombus right angles right-angled triangle segment shew shewn side BC square on AC straight line &c straight line drawn tangent THEOREM touches the circle triangle ABC triangle DEF twice the rectangle vertex Wherefore
Beliebte Passagen
Seite 262 - 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.
Seite 71 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a Right Angle; and the straight line which stands on the other is called a Perpendicular to it.
Seite 262 - To draw a straight line at right angles to a given straight line, from a given point in the same. Let AB be...
Seite 182 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Seite 8 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Seite 298 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Seite 58 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Seite 60 - If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together double of AD»+DB
Seite 242 - Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB.
Seite 4 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.