1. Gothic versus Romanesque Architecture
The earliest churches were based on Greek temples and Roman basilicas (secular government buildings); essentially there was a substitution of a church plan for a temple plan: colonnades were shifted from the interior to the exterior; an arch was placed directly on a pier instead of placing a lintel directly on a pier (column)
The classic temple is a system of sturdy walls and colonnades all helping to sustain a solid roof. A Romanesque church follows essentially the same principles, except that an arch is placed over the colonnades.
All the parts of a Romanesque building contribute their share to the stability of the whole.
The structure stands through virtue of inertia.
Gothic
In a Gothic church the highly organized framework of piers, arches, and buttresses are organized so that the spaces of the wall and roof between them serve merely as an enclosure.
A Gothic church is a skillfully balanced systems of thrusts and counterthrusts that are concentrated on special points of support.
All the different levels of the church interior are brought into homogenous composition: great vaulting shafts that articulate the massive piers rise from the floor; at the clerestory level these shafts become more decorative than supportive and spring from corbels in order to trace the vaulting that articulates each bay.
Flying buttresses allowed the walls to be dissolved.

2. Roman barrel vault
The force lines converge at the point where the barrel vault springs from the wall.
In order to support a heavy roof—one that is very wide--the walls of the nave would have to be very, very thick.
Flying Buttress
The lines of force created by the weight of the roof and the arches is redirected (or distributed) by the flying buttresses past the walls of the church to external piers (outside the child walls). As a result, windows can larger and the nave can be taller.

3. Abbey Church of Saint-Denis Saint-Denis, France 1140-44

4. floor plan Abbey Church of Sainte-Foy Conques, France 1125-1135

5. Abbey Church of Saint-Denis Saint-Denis, France 1140-44
Standing in the choir, looking northeast at about 1:30.

6. Abbey Church of Saint-Denis Saint-Denis, France 1140-44
Looking into one of the radial chapels.

7. floor plan Abbey Church of Sainte-Foy Conques, France 1125-1135
floor plan Amiens Cathedral Amiens, France

8. Abbey Church of Sainte-Foy Conques, France 1125-1135

9. Abbey Church of Sainte-Foy Conques, France 1125-1135

10. transept looking into the crossing Amiens Cathedral Amiens, France 1220-1288

11. standing on the steps of the choir looking into the apse Amiens Cathedral Amiens, France 1220-1288

12. looking down the nave toward the apse Amiens Cathedral Amiens, France 1220-1288

13. Abbey Church of Sainte-Foy Conques, France 1125-1135
Amiens Cathedral Amiens, France

14. Church of Saint-Etienne, Caen Normandy, France
begun 1064—façade late 11th century

15. Chartres Cathedral ca. 1194-1260
west façade

16. Reims Cathedral
west façade c