## A Royal Road to Geometry: Or, an Easy and Familiar Introduction to the Mathematics. ... By Thomas Malton. ... |

### From inside the book

Results 1-5 of 5

Page 14

A

Z. N.B. All Rectangles and Squares are

is a

A

**PARALLELOGRAM**is a Quadrilateral , whose opposite Sides are parallel . ...Z. N.B. All Rectangles and Squares are

**Parallelograms**. DEF . 36. A RHOMBUSis a

**Parallelogram**, whose Sides are all equal , and its Angles not Right ones . 2. Page 144

Altitudes , are equal . B В с F Th . 15 Ax . The

**Parallelograms**, or Triangles , having the fame or equal Bases , and equalAltitudes , are equal . B В с F Th . 15 Ax . The

**Parallelogram**ABCD is equal to the**Parallelogram**AFGD ; standing on the same Base A D ; and between the same ... Page 309

wherefore , the Sides of the

Sides proportional . But , the Angle EAH is ... Consequently , the Par . FICG is

similar to AEFH ; being both similar to the whole

wherefore , the Sides of the

**Parallelograms**Ą E F H , and ABCD , have all theirSides proportional . But , the Angle EAH is ... Consequently , the Par . FICG is

similar to AEFH ; being both similar to the whole

**Parallelogram**, ABCD -Axiom . Page 310

If a

a

equiangular to the first ; that , which is described on the half Line , is greater than

...

If a

**Parallelogram**be described on a Right Line , and from it there be taken awaya

**Parallelogram**, similar , and alike situated , to one described on half the Line ,equiangular to the first ; that , which is described on the half Line , is greater than

...

Page 311

From the lesser

Diameter , in the

; and Gc ...

From the lesser

**Parallelogram**A b c D , lec there be taken away the**Parallelogram**hic D , fimilar to AEFG , and situate alike . Now , because F D is aDiameter , in the

**Parallelogram**GFKD , Gi is equal to i K. Add hicD , on both sides; and Gc ...

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### Common terms and phrases

ABCD added alſo Altitudes analogous Area Baſe becauſe biſected Book called Center Chord Circle Circumference common Cone conf conſequently Conſtruction contained cuting Cylinder Demonſtration deſcribe Diagonal Diameter difference divided draw drawn equal Euclid evident extreme fame Feet Figure firſt formed four fourth given given Line greater half Hence Inches inſcribed join laſt leſs manner mean meaſure multiplied muſt oppoſite parallel Parallelogram Parallelopiped Pentagon perpendicular Plane Point Poligon Priſm Prob PROBLEM produced Proportion Propoſition proved Pyramid Quantities Radius Ratio Rect Rectangle reſpectively Right Angles Right Line ſame ſame Ratio ſay ſeeing Segment Sides ſimilar Solid ſome Sphere Square ſuch Surface taken Terms THEOREM third thoſe touch Triangle uſe wherefore whole whoſe

### Popular passages

Page 124 - When you have proved that the three angles of every triangle are equal to two right angles...

Page 221 - 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.

Page 285 - EG, let fall from a point in the circumference upon the diameter, is a mean proportional between the two segments of the diameter DS, EF (p.

Page 284 - IN a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles on each side of it are similar to the whole triangle, and to one another.

Page 186 - From this it is manifest, that if one angle of a triangle be equal to the other two, it is a right angle, because the angle adjacent to it is equal to the same two; and when the adjacent angles are equal, they are right angles.

Page 248 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.

Page 161 - In any triangle, if a line be drawn from the vertex at right angles to the base; the difference of the squares of the sides is equal to the difference of the squares of the segments of the base.

Page 160 - In any isosceles triangle, the square of one of the equal sides is equal to the square of any straight line drawn from the vertex to the base plus the product of the segments of the base.

Page 250 - Ratios that are the same to the same ratio, are the same to one another. Let A be to B as C is to D ; and as C to D, so let E be to F.

Page 124 - Angles, taken together, is equal to Twice as many Right Angles, wanting four, as the Figure has Sides.