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, 1867 - 400 σελίδες |
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Σελίδα xiii
... ook I. ook II . ook III . ook IV . XV I 52 71 113 ook V ........ 134 ook VI . 173 ook XI . 220 ook XII .. 244 otes on Euclid's Elements 250 -ppendix 292 xercises in Euclid 340 INTRODUCTORY REMARKS . THE subject of Plane Geometry is here.
... ook I. ook II . ook III . ook IV . XV I 52 71 113 ook V ........ 134 ook VI . 173 ook XI . 220 ook XII .. 244 otes on Euclid's Elements 250 -ppendix 292 xercises in Euclid 340 INTRODUCTORY REMARKS . THE subject of Plane Geometry is here.
Σελίδα xiv
... Todhunter. THE student into pr blems to be d be true A the ge examp finite s togethe enunci the en figure be the equila follows which the pr of the which theore Sor Someti bined . INTRODUCTORY REMARKS . THE subject of Plane Geometry is ...
... Todhunter. THE student into pr blems to be d be true A the ge examp finite s togethe enunci the en figure be the equila follows which the pr of the which theore Sor Someti bined . INTRODUCTORY REMARKS . THE subject of Plane Geometry is ...
Σελίδα xv
... Plane Geometry is here presented to the student arranged in six books , and each book is subdivided into propositions . The propositions are of two kinds , pro- blems and theorems . In a problem something is required to be done ; in a ...
... Plane Geometry is here presented to the student arranged in six books , and each book is subdivided into propositions . The propositions are of two kinds , pro- blems and theorems . In a problem something is required to be done ; in a ...
Σελίδα 1
... plane superficies is that in which any two points being taken , the straight line between them lies wholly in that superficies . 8. A plane angle is the inclination of two lines to one another in a plane , which meet together , but are ...
... plane superficies is that in which any two points being taken , the straight line between them lies wholly in that superficies . 8. A plane angle is the inclination of two lines to one another in a plane , which meet together , but are ...
Σελίδα 2
... plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . Note . When several angles are at one point B , any one of them is expressed by three ...
... plane rectilineal angle is the inclination of two straight lines to one another , which meet together , but are not in the same straight line . Note . When several angles are at one point B , any one of them is expressed by three ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD angle ABC angle ACB angle BAC angle EDF angles equal Axiom base BC BC is equal 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
Δημοφιλή αποσπάσματα
Σελίδα 286 - 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.
Σελίδα 30 - 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...
Σελίδα 34 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles...
Σελίδα 37 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.
Σελίδα 12 - 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.
Σελίδα 302 - Describe a circle which shall pass through a given point and touch a given straight line and a given circle.
Σελίδα 220 - If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 354 - Prove that the square on any straight line drawn from the vertex of an isosceles triangle to the base, is less than the square on a side of the triangle by the rectangle contained by the segments of the base : and conversely.
Σελίδα 104 - 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.
Σελίδα 96 - The opposite angles of any quadrilateral figure inscribed in a circle, are together equal to two right angles.