The Elements of geometry; or, The first six books, with the eleventh and twelfth, of Euclid, with corrections, annotations, and exercises, by R. Wallace. Cassell's ed1855 |
Im Buch
Ergebnisse 6-10 von 66
Seite 19
... shown that B A , AC are greater than BE , EC . B Much more then are B A , AC , greater than BD , DC . Again , the exterior angle BDC of the triangle CDE is greater than its interior and opposite angle CED ( I. 16 ) . And the exterior ...
... shown that B A , AC are greater than BE , EC . B Much more then are B A , AC , greater than BD , DC . Again , the exterior angle BDC of the triangle CDE is greater than its interior and opposite angle CED ( I. 16 ) . And the exterior ...
Seite 22
... shown that the angle BAC is not equal to the angle EDF . Therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. Corollary . If two triangles have two sides of the one respectively equal to ...
... shown that the angle BAC is not equal to the angle EDF . Therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. Corollary . If two triangles have two sides of the one respectively equal to ...
Seite 27
... shown to be equal to the angle B AC . Therefore the whole exterior angle A CD is equal ( 4x . 2 ) to the two interior and opposite angles CAB , ABC . To each of these equals , add the angle A CB . Therefore the two angles ACD , ACB are ...
... shown to be equal to the angle B AC . Therefore the whole exterior angle A CD is equal ( 4x . 2 ) to the two interior and opposite angles CAB , ABC . To each of these equals , add the angle A CB . Therefore the two angles ACD , ACB are ...
Seite 27
... shown to be equal to the angle BA C. Therefore the whole exterior angle ACD is equal ( Ax . 2 ) to the two interior and opposite angles CAB , ABC . To each of these equals , add the angle A CB . Therefore the two angles ACD , ACB are ...
... shown to be equal to the angle BA C. Therefore the whole exterior angle ACD is equal ( Ax . 2 ) to the two interior and opposite angles CAB , ABC . To each of these equals , add the angle A CB . Therefore the two angles ACD , ACB are ...
Seite 51
... shown by Dr. Thomson that A B is the greater of the two straight lines A B and AF . But the same defect lurks in the demonstration of Euclid . Corollary 1. - In the figure to this proposition , the straight line CF is cut at the point A ...
... shown by Dr. Thomson that A B is the greater of the two straight lines A B and AF . But the same defect lurks in the demonstration of Euclid . Corollary 1. - In the figure to this proposition , the straight line CF is cut at the point A ...
Andere Ausgaben - Alle anzeigen
The Elements of Geometry: Or, the First Six Books, with the Eleventh and ... Euclides Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angle DEF angle EDF base BC bisected centre circle ABC circumference cone cylinder described diagonal diameter draw duplicate ratio equal angles equal Ax equal Const equiangular equimultiples Euclid ex æquali Exercise exterior angle fore given straight line gnomon homologous sides inscribed join less meet multiple opposite angle parallelogram parallelogram AC parallelopiped pentagon perpendicular polygon prism produced proposition Q. E. D. PROP reciprocally proportional rectangle contained rectilineal figure remaining angle right angles segment similar triangles solid angle sphere squares of AC straight line drawn straight lines A B THEOREM third three plane angles three straight lines triangle ABC triangle DEF triplicate ratio twice the rectangle vertex Wherefore whole angle
Beliebte Passagen
Seite 23 - 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 34 - If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line.
Seite 2 - 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 122 - 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 5 - LET it be granted that a straight line may be drawn from any one point to any other point.
Seite 3 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Seite 135 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing those angles proportional, are similar.
Seite 20 - PROBLEM. At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle.
Seite 147 - Similar solid figures are such as have all their solid angles equal, each to each, and are contained by the same number of similar planes.
Seite 37 - If a straight line be bisected, and produced to any point ; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square...