The First Book of Euclid's Elements: Arranged for BeginnersMacMillan, 1892 - 167 sider |
Inni boken
Resultat 1-5 av 15
Side 15
... fall somewhere on the straight line of which CA is a finite portion . When in what follows , we use the phrase ' the point P falls on the line CA ' it is used as an abbreviation for ' the point P falls on the straight line of which CA ...
... fall somewhere on the straight line of which CA is a finite portion . When in what follows , we use the phrase ' the point P falls on the line CA ' it is used as an abbreviation for ' the point P falls on the straight line of which CA ...
Side 20
... fall on E ; also , the point A is on D and the point C is on the line DF ; then , because AC is equal to DF , therefore C must fall on F. Thus , the three points A , B , C fall on the three points D , E , F respectively ; so that the ...
... fall on E ; also , the point A is on D and the point C is on the line DF ; then , because AC is equal to DF , therefore C must fall on F. Thus , the three points A , B , C fall on the three points D , E , F respectively ; so that the ...
Side 24
... can be proved , as in Proposition 4 , that the triangle FDE can be applied to the triangle BAC so that the points F , D , E shall fall on the points B , A , C respectively . Then the angle DEF coincides with the angle ACB and 24 EUCLID .
... can be proved , as in Proposition 4 , that the triangle FDE can be applied to the triangle BAC so that the points F , D , E shall fall on the points B , A , C respectively . Then the angle DEF coincides with the angle ACB and 24 EUCLID .
Side 25
... fall upon B , A , C respectively , it follows , that the angle LFE can be made to coincide with GBC , and is therefore equal to it . But the angle LFE is equal to HCB ; therefore the angle GBC is equal to the angle HCB . Q.E.D. Euclid's ...
... fall upon B , A , C respectively , it follows , that the angle LFE can be made to coincide with GBC , and is therefore equal to it . But the angle LFE is equal to HCB ; therefore the angle GBC is equal to the angle HCB . Q.E.D. Euclid's ...
Side 28
... fall on the straight line of which FD is a finite portion . Thus the point A falls on both the straight lines ED and FD therefore the point A must fall on D , the only point common to both these lines ED , FD . Thus the points A , B , C ...
... fall on the straight line of which FD is a finite portion . Thus the point A falls on both the straight lines ED and FD therefore the point A must fall on D , the only point common to both these lines ED , FD . Thus the points A , B , C ...
Vanlige uttrykk og setninger
ABC is equal adjacent angles alternate angles angle ABC angle ACB angle BAC angle equal angles FAB angular point area of ABC base BC bisectors bisects the angle centre coincide Consider the triangles Construction corresponding angle DEF are equal describe a triangle diagonal equal angles equal area equal in area equal respectively equal to BC equidistant equilateral triangle exterior angle finite straight line given angle given finite straight given parallelogram given point given straight line given triangle greater included angle interior opposite angle intersect isosceles triangle line BC middle point opposite sides perpendicular plane produced Prop Proposition Q.E.D. EXAMPLES quadrilateral radius rectilineal figure required to prove rhombus right angles right-angled triangle Shew side BC sides equal square straight angle surface third side triangle ABC triangle DEF triangles are equal Wherefore
Populære avsnitt
Side 28 - 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.
Side 72 - If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Side 48 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Side 151 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Side 118 - THE straight lines which join the extremities of two equal and parallel straight lines, towards the same parts, are also themselves equal and parallel.
Side 149 - ... is equal to the sum of the areas of the squares on the other two sides.
Side 114 - 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.
Side 135 - DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i.
Side 125 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Side 54 - To draw a straight line at right angles to a given straight line, from a given point in the same.