The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With Notes and Illustrations, and an Appendix in Five BooksA. & C. Black, 1837 - 390 Seiten |
Im Buch
Ergebnisse 1-5 von 32
Seite 16
... vertical angles would be proved by means of the third axiom . 66 The expression , on the side remote from A , " is added in this edition , because , if the equilateral triangle were described on the other side its vertex might fall on A ...
... vertical angles would be proved by means of the third axiom . 66 The expression , on the side remote from A , " is added in this edition , because , if the equilateral triangle were described on the other side its vertex might fall on A ...
Seite 20
... vertical , or opposite , angles are equal . A- B E D Let the two straight lines AB , CD cut one another in E ; the angle AEC is equal to the angle DEB , and CEB to AED . Because the straight line AE , makes with CD C the angles CEA ...
... vertical , or opposite , angles are equal . A- B E D Let the two straight lines AB , CD cut one another in E ; the angle AEC is equal to the angle DEB , and CEB to AED . Because the straight line AE , makes with CD C the angles CEA ...
Seite 21
... vertical angles ; therefore the angle BAE is equal ( I. 4. part 3. ) to ECF ; but the angle ECD is greater ( I. ax . 9. ) than ECF ; therefore the angle ACD is greater than BAE . In the same manner , if the side AC be produced ( I. post ...
... vertical angles ; therefore the angle BAE is equal ( I. 4. part 3. ) to ECF ; but the angle ECD is greater ( I. ax . 9. ) than ECF ; therefore the angle ACD is greater than BAE . In the same manner , if the side AC be produced ( I. post ...
Seite 35
... vertical angle made by producing BA , CA , through A , are each equal to D ; while the angle made by BA and the continu- ation of CA , or by CA and the continuation of BA , is equal to the supplement ( I. def . 38. ) of D. * The ...
... vertical angle made by producing BA , CA , through A , are each equal to D ; while the angle made by BA and the continu- ation of CA , or by CA and the continuation of BA , is equal to the supplement ( I. def . 38. ) of D. * The ...
Seite 139
... vertical angle . 1. Let the angle BAC of the triangle ABC be bisected by the straight line AD ; BD : DC : : BA : AC . E Through C draw ( I. 31. ) CE parallel to DA : then ( I. 29 . cor . 1. ) BA produced will meet CE ; let them meet in ...
... vertical angle . 1. Let the angle BAC of the triangle ABC be bisected by the straight line AD ; BD : DC : : BA : AC . E Through C draw ( I. 31. ) CE parallel to DA : then ( I. 29 . cor . 1. ) BA produced will meet CE ; let them meet in ...
Andere Ausgaben - Alle anzeigen
The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ... Euclid Keine Leseprobe verfügbar - 2016 |
Häufige Begriffe und Wortgruppen
ABCD altitude angle ABC angle BAC angle equal BC is equal bisected centre chord circle ABC circumference cone const contained cylinder describe a circle diagonal diameter divided draw equal angles equal to AC equiangular equilateral Euclid exterior angle fore fourth given circle given point given ratio given straight line greater half Hence hypotenuse inscribed join less Let ABC magnitudes manner multiple opposite parallel parallelepiped parallelogram perpendicular polygon polyhedron prism PROB produced PROP proportional proposition pyramid radius rectangle rectilineal figure right angles Schol segments semicircle sides similar similar triangles solid angles square of AC straight lines drawn tangent THEOR third triangle ABC triplicate ratio vertex vertical angle wherefore
Beliebte Passagen
Seite 94 - 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 53 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Seite 143 - 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 4 - A rhombus is that which has all its sides equal, but its angles are not right angles.
Seite 57 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part.
Seite 138 - IF a straight line be drawn parallel to one of the sides of a triangle, it shall cut the other sides, or those produced, proportionally; and if the sides, or the sides produced, be cut proportionally, the straight line which joins the points of section shall be parallel to the remaining side of the triangle...
Seite 43 - In any right-angled triangle, the square which is described upon the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle.
Seite 32 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Seite 40 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Seite 36 - PARALLELOGRAMS upon the same base, and between the same parallels, are equal to one another...